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Substitution method 2 | Systems of equations | 8th grade | Khan Academy

Video vocabulary

number

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US / ˈnʌmbə(r) /

UK / ˈnʌmbɚ /

A1
  • noun
  • Symbols such as 1, 2, 56, 793
  • Particular song or dance performed during a show
  • Total quantity or amount of things
  • verb
  • To put numbers on things
  • To assign a sequence within a group, series, set
  • To claim to be part of a larger group, series, set

tell

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US / tel /

UK / tɛl /

A1
  • verb
  • To (strongly) advise a person to do something
  • To be able to guess
  • To say or communicate information to someone
  • To inform, but without speaking; indicate
  • To have a negative effect on someone
  • To order someone to do something; command
  • To recognize something based on certain signs
  • To report something to an authority
  • To explain something or teach someone something

solve

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US / sɒlv /

UK / sɑ:lv /

A2
  • verb
  • To figure out a way to handle a difficult problem

constraint

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US / kənˈstreɪnt /

UK / kənˈstrent /

B1
  • noun
  • Thing preventing you moving or acting; restriction

different

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US / ˈdɪfrənt /

UK / ˈdɪfrənt /

A1
  • adjecitve
  • Not of the same kind; unlike other things

like

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US / laɪk /

UK / laɪk /

A1
  • adjecitve
  • Being equal in status or kind to something else
  • Similar; the same
  • adverb
  • For example
  • preposition
  • Used as a filler; used to ad emphasis
  • In a way similar to the way something is done
  • Such as; for example
  • verb
  • To want to
  • To find something pleasing; to prefer something

that

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US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

steep

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US / sti:p /

UK / stip /

B1
  • adjecitve
  • Very expensive
  • Rising or falling very sharply, as a cliff or hill
  • Involving a quick increase or decrease
  • verb
  • To fill with a certain quality, e.g. history
  • To put a thing in a liquid for some time

what

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US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

everywhere

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US / ˈevriweə(r) /

UK / ˈevriwer /

A1
  • adverb
  • Every place

right

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US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

mean

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US / mi:n /

UK / min /

A1
  • adjecitve
  • Being good at
  • Nasty; unkind
  • Not liking to spend money; cheap; stingy
  • noun
  • Average of a set of numbers
  • verb
  • To express a particular idea or thought
  • To intend to do something in particular
  • To have a particular meaning or value

down

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US / daʊn /

UK / daʊn /

A1
  • adjecitve
  • Being sad, sick, or unhappy
  • Not operating, working, or functioning as expected
  • adverb
  • In a sitting or lying position
  • Towards or on the ground, floor, or bottom
  • Written or copied onto a piece of paper or book
  • noun
  • A period of play in American Football
  • The soft, smooth hairs that cover a bird's body
  • preposition
  • Along something's path, course, or direction
  • Going from a higher position to a lower position
  • verb
  • To eat or drink very quickly and without stopping

must

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US / məst /

UK / mʌst /

A1
  • noun
  • Something that is necessary or required
  • other
  • (Used to state that something ought to be true)
  • Used to say something is required or necessary

then

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US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

whenever

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US / wenˈevə(r) /

UK / hwɛnˈɛvɚ /

A1
  • adverb
  • At any or every time that

first

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US / fɜ:st /

UK / fɚst /

A1
  • adjecitve
  • 1st; Coming before all others in time or place
  • noun
  • Something that has not happened before
  • Position of the winner of a competition

get

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US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

second

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US / 'sekənd /

UK / ˈsɛkənd /

A1
  • adjecitve
  • 2nd; the one following first
  • noun
  • Unit of time; one sixtieth of a minute
  • Short period of time that you wait for someone
  • (Do) soon
  • verb
  • To agree to support a proposal at a meeting

crazy

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US / 'kreɪzɪ /

UK / ˈkrezi /

A2
  • adjecitve
  • Mentally ill; mad
  • Not being sensible or practical
  • Really like someone or something very much
  • noun
  • Person acting in a manner that is strange and odd

want

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US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

same

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US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant

wacky

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US / 'wækɪ /

UK / ˈwæki /

A1
  • adjecitve
  • Quite strange, but in a creative way

but

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US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

give

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US / ɡɪv /

UK / ɡɪv /

A1
  • noun
  • Degree of flexibility in something, a material
  • verb
  • To hand over or present something to someone
  • To cause someone to have or experience something

really

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US / ˈri:əli /

UK / ˈriəˌli, ˈrili /

A1
  • adverb
  • Used to stress something that is said; definitely
  • In a true or accurate manner
  • Very

distribute

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US / dɪˈstrɪbju:t /

UK / dɪˈstrɪbjut /

A2
  • verb
  • To hand out or give to people
  • To send products to stores to sell
  • To spread something over an area

not

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US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

our

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US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

equal

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US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

now

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US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

substitute

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US / 'sʌbstɪtju:t /

UK / ˈsʌbstɪˌtut, -ˌtjut /

B2
  • noun
  • A person or thing acting in place of another
  • verb
  • To perform the tasks instead of someone else
  • To replace one person or thing for another

can

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US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

equation

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US / ɪˈkweɪʒn /

UK / ɪˈkweʒən, -ʃən /

B1
  • noun
  • Mathematical statement showing things to be equal
  • Complex set of different facts, ideas or issues

graph

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US / græf /

UK / ɡræf /

A2
  • noun
  • Image expressing numerical data in lines or shapes
  • verb
  • To show data using images

for

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US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

time

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US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

why

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US / waɪ /

UK / hwaɪ, waɪ /

A1
  • adverb
  • Question word to ask for a reason
  • exclamation
  • (Used to express surprise or approval)

just

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US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

line

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US / laɪn /

UK / laɪn /

A1
  • noun
  • Border that divides two places or regions
  • Long crease in the skin, often from age
  • Mark that is long, straight and very thin
  • Row of words, letters or numbers that are written
  • Telephone connection
  • People waiting one behind the other; queue
  • Long thin wire, e.g. for electrical signal
  • verb
  • To put material along the inside of something

those

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US / ðəʊz /

UK / ðoz /

A1
  • determiner
  • The people or things we are talking about
  • pronoun
  • The objects far from the speaker

set

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US / set /

UK / sɛt /

A1
  • adjecitve
  • Prepared for something; ready
  • noun
  • Complete group of something
  • Place where a television show or movie is filmed
  • Group of games in a tennis match
  • Device that receives radio or television signals
  • verb
  • To make a clock state or ring at a particular time
  • To decide upon or choose something
  • To make something ready for use (e.g. table)
  • To decide on a price for something
  • To become hard (of glue, concrete etc.)
  • To be located in a specific place or time
  • To put (e.g. a vase) down carefully in a place
  • To put someone in a certain condition or state
  • (Of the sun) to go lower than the horizon

well

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US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears

explicitly

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US / ɪk'splɪsɪtlɪ /

UK / ɪk'splɪsɪtlɪ /

B1
  • adverb
  • Clearly; specifically

system

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US / 'sɪstəm /

UK / ˈsɪstəm /

A1
  • adjecitve
  • Working in an organized, logical way
  • noun
  • Set of organized, planned ideas that work together

slope

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US / sləʊp /

UK / sloʊp /

B1
  • noun
  • Angle of a decline, e.g. where a road dips down
  • Surface on which people can ski
  • verb
  • To have one end that is not as high as the other

solution

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US / səˈlu:ʃn /

UK / səˈluʃən /

A2
  • noun
  • Mix of a liquid and a solid or a gas
  • Way to solve or deal with a problem

forward

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US / 'fɔ:wəd /

UK / ˈfɔrwəd /

A1
  • adjecitve
  • Toward what is ahead; in front
  • Acting in a socially aggressive manner; pushy
  • adverb
  • Toward the front in place; in front
  • Toward a future time; to a more advanced state
  • verb
  • To send something to another address or person

other

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US / 'ʌðə(r) /

UK / ˈʌðər /

A1
  • adjecitve
  • A thing different from that mentioned
  • determiner
  • (Something) else; not the first (one)
  • pronoun
  • Being the one and only thing of that category

one

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US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

make

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US / meɪk /

UK / mek /

A1
  • noun
  • Product made by a particular company; brand
  • verb
  • To arrange or prepare something e.g. dinner
  • To get to (a place) on time
  • To gain the status of (teacher, lawyer, etc.)
  • To create something by putting things together
  • To earn a certain amount of money at a job
  • To cause or force a person to do something
  • To cause something to happen or be formed

repetitive

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US / rɪˈpetətɪv /

UK / rɪˈpɛtɪtɪv /

B2
  • adjecitve
  • Doing or saying the same things many times

multiple

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US / ˈmʌltɪpl /

UK / ˈmʌltəpəl /

B1
  • adjecitve
  • Having or involving more than one of something
  • noun
  • Number produced by multiplying a smaller number
  • Shop with many branches

term

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US / tɜ:m /

UK / tɚm /

A1
  • noun
  • Conditions applying to an agreement, contract
  • Length of time something is expected to happen
  • Fixed period of weeks for learning at school
  • The (precise) name given to something
  • verb
  • To call; give a name to

this

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US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

let

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US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

the

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US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

clearly

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US / ˈklɪəlɪ /

UK / ˈklɪrlɪ /

A1
  • adverb
  • In a way that is easy to understand; obviously

pretty

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US / 'prɪtɪ /

UK / ˈprɪti /

A1
  • adjecitve
  • Being attractive to the eye in a simple way
  • adverb
  • Very; to a great degree

subtract

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US / səbˈtrækt /

UK / səbˈtrækt /

B2
  • other
  • To take away a value or amount from another
  • verb
  • To take away a value or amount from another

they

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US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

very

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US / 'verɪ /

UK / ˈvɛri /

A1
  • adjecitve
  • Concerning a large degree or amount
  • adverb
  • A lot; much; many
  • Used to stress or emphasize a noun

both

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US / bəuθ /

UK / boθ /

A1
  • determiner
  • Used to refer to two things at the same time
  • pronoun
  • Used to refer to two things at the same time

result

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US / rɪ'zʌlt /

UK / rɪˈzʌlt /

A2
  • noun
  • Something produced through tests or experiments
  • Final score of a competition, election or game
  • verb
  • To be the outcome of other causes and effects

bit

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US / bɪt /

UK / bɪt /

A1
  • noun
  • Device put in a horse's mouth to control it
  • Small piece of something
  • verb
  • (E.g. of fish) to take bait and be caught

cancel

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US / 'kænsl /

UK / ˈkænsəl /

A2
  • verb
  • To end a legal, business, or other agreement
  • To stop a planned event from happening

look

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US / lʊk /

UK / lʊk /

A1
  • noun
  • Person's beauty or physical attractiveness
  • Particular style of dress, clothes, or appearance
  • The way someone, something appears to be
  • Act of searching for or examining something
  • verb
  • To appear to be; seem

multiply

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US / ˈmʌltɪplaɪ /

UK / ˈmʌltəˌplaɪ /

B1
  • verb
  • To increase in number by reproducing/having babies
  • To increase something by a large quantity
  • To have increased by a large quantity
  • To calculate two numbers e.g. 2 x 4

rewrite

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US / ˌri:'raɪt /

UK / riˈraɪt /

A2
  • verb
  • To write again to improve, or correct errors

move

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US / mu:v /

UK / muv /

A1
  • noun
  • Act of moving a playing piece in chess, etc.
  • An action; doing something
  • Step taken to achieve a goal
  • verb
  • To cause someone to have certain emotions
  • To cause something to change to a different place
  • To change where people live or a business operates
  • To take action to do or achieve something

all

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US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

already

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US / ɔ:lˈredi /

UK / ɔlˈrɛdi /

A1
  • adverb
  • Having happened or been done before this time

telltale

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US / ˈtelteɪl /

UK / ˈtɛlˌtel /

C2
  • noun
  • Someone who discloses information intentionally

shift

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US / ʃɪft /

UK / ʃɪft /

A2
  • adjecitve
  • (Of work) starting at a certain time, as at night
  • noun
  • A change in a persons plans, opinions or beliefs
  • Period of work starting at a certain time
  • verb
  • To change in position or direction
  • To move something from one place to another

inconsistent

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US / ˌɪnkənˈsɪstənt /

UK / ˌɪnkənˈsɪstənt /

B1
  • adjecitve
  • Not tying together logically or with the facts

divide

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US / dɪ'vaɪd /

UK / dɪˈvaɪd /

A2
  • verb
  • To split numbers by another number, e.g. 6 / 2 = 3
  • To separate something into equal pieces

satisfy

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US / ˈsætɪsfaɪ /

UK / ˈsætɪsˌfaɪ /

A2
  • verb
  • To make someone happy because they got their wish
  • To do what is required in order to finish

actually

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US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

use

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US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
  • Need to enable it to work
  • Permission to do something with something
  • Act of spending money
  • Operation of a machine for its function
  • verb
  • To have; to eat, drink, consume etc.
  • To need to operate or work
  • To operate a machine, e.g. a computer
  • To treat a person badly
  • To do something with, for a task or purpose

write

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US / raɪt /

UK / raɪt /

A1
  • verb
  • To compose letters and words on paper or a screen
  • To invent or create a computer program
  • To create a song or piece of music

here

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US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

intersect

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US / ˌɪntə'sekt /

UK / ˌɪntɚˈsɛkt /

B2
  • verb
  • To divide something by crossing it

plus

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US / plʌs /

UK / plʌs /

A2
  • noun
  • A benefit or advantage
  • preposition
  • In addition; add
  • In addition to; Indicates a number above
  • Having a value greater than zero

side

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US / saɪd /

UK / saɪd /

A1
  • adjecitve
  • In addition to the central or most important thing
  • Next to, or very close to, the right or left of
  • noun
  • Position or opinion that is opposite to another
  • Right or left part of a person's body
  • Feature of someone's personality
  • Straight edge of an object
  • One of two or more groups fighting each other
  • verb
  • To decide to agree with one point, not the other

negative

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US / 'neɡətɪv /

UK / ˈnɛɡətɪv /

A2
  • adjecitve
  • Being harmful, unwanted or unhelpful
  • In mathematics, being less than zero
  • Focusing on the bad aspects; pessimistic
  • noun
  • The opposite to a positive electrical charge
  • In grammar, containing words such as 'no' or 'not'
  • Reply to a question or statement that means 'no'
  • Image on camera film used to make a photo

onto

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US / ˈɒntə /

UK / ˈɑnˌtu, -tə, ˈɔn- /

A1
  • preposition
  • Towards a certain direction/into a certain area

see

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US / si: /

UK / si /

A1
  • verb
  • To go on a date with someone
  • To predict whether something is, or will be true
  • To understand what someone says
  • To use your eyes to look at something
  • To visit a place often for sightseeing or pleasure
  • To visit or meet with someone
  • To find out by waiting or looking
  • To watch (a game, movie or TV show)

clear

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US / klɪə(r) /

UK / klɪr /

A1
  • adjecitve
  • Empty; without anything in it or on it
  • Being certain and without doubt
  • Being without any streaks, spots, or cracks
  • Easy to understand; well-explained; obvious
  • adverb
  • Completely; entirely; through the whole of
  • Away from; free from
  • verb
  • To recover from or remove a problem
  • To get rid of the entire contents of
  • To give permission for something to happen
  • To make a place or surface empty by removing
  • To prove that someone is not guilty or to blame

algebraically

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US / ˌældʒɪˈbreɪkli /

UK / ˌældʒəˈbreɪɪkli /

C1
  • adverb
  • In an algebraic manner

could

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US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

know

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US / nəʊ /

UK / noʊ /

A1
  • verb
  • To be familiar with a person or place, thing
  • To feel sure or be convinced about something
  • To discover or be aware of something
  • To be able to distinguish
  • To have knowledge of things

have

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US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

parallel

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US / 'pærəlel /

UK / ˈpærəˌlɛl /

B1
  • adjecitve
  • (Of two lines) at equal distance from each other
  • (Of computer operation) happening at the same time
  • Very similar and often occurring at the same time
  • noun
  • A line on a map a set distance from the equator
  • verb
  • To be equal to, or like, something else
  • To compare

with

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US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

call

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US / kɔ:l /

UK / kɔl /

A1
  • noun
  • A order or request for action
  • The sound an animal makes, often when in danger
  • A correct prediction, e.g. a decision in a game
  • A short visit to a place or person
  • A decision by a referee or umpire in a game
  • verb
  • To make a request or order for action
  • (Animal) to make sounds to warn of danger
  • To announce the date of an election
  • To make a judgment about something
  • To give someone or something a name
  • To guess in advance the result or outcome
  • To visit a place or person for a short time
  • To phone someone
  • To speak, announce or shout in a loud voice

leave

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US / li:v /

UK / liv /

A1
  • noun
  • Permission to do something
  • Vacation time; time off work
  • verb
  • To go away from; depart
  • To gift property to someone after you die
  • To allow something to continue happening
  • To let something remain unused or available
  • To let something or someone remain somewhere

from

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US / frəm /

UK / frʌm, frɑm,frəm /

A1
  • preposition
  • Starting at a particular place, time or level

form

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US / fɔ:m /

UK / fɔrm /

A1
  • noun
  • Sports team or person's current winning record
  • Document you complete when making an application
  • Visible shape or style; type; kind
  • verb
  • To organize something such as a club or group
  • To develop; to come into a shape or substance
  • To make something into a particular shape

internalize

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US / ɪnˈtɜ:nəlaɪz /

UK / ɪnˈtɜ:rnəlaɪz /

B1
  • verb
  • To accept attitudes, behavior as part of yourself

out

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US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

over

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US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

minus

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US / ˈmaɪnəs /

UK / ˈmaɪnəs /

A2
  • adjecitve
  • Being close to the bottom of a letter grade
  • noun
  • Negative quality; disadvantage
  • Sign that indicates subtraction
  • preposition
  • Being less than zero in number
  • Used when subtracting one number from another
  • verb
  • To take one number away from another; subtract

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

something

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US / ˈsʌmθɪŋ /

UK / ˈsʌmθɪŋ /

A1
  • adverb
  • In some degree or measure
  • noun
  • a person or thing of some value or consequence
  • pronoun
  • Thing that is not yet known or named
  • Approximately

and

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US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

guy

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US / ɡaɪ /

UK / ɡaɪ /

A1
  • noun
  • Man; boy; any person
  • Subtitles section
  • Use substitution to solve for x and y.
  • And they give us a system of equations here. y is equal to negative 5x plus 8 and 10x plus 2y is equal to negative 2.
  • So they've set it up for us pretty well.
  • They already have y explicitly solved for up here.
  • So they tell us, this first constraint tells us that y must be equal to negative 5x plus 8.
  • So when we go to the second constraint here, every time we see a y, we say, well, the first constraint tells us that y must be equal to negative 5x plus 8.
  • So everywhere we see a y, we can substitute it with negative 5x plus 8.
  • Because that's what the first constraint tells us.
  • y is equal to that.
  • I don't want to be repetitive, but I really want you to internalize that's all it's saying. y is that.
  • So every time we see a y in the second constraint, we can substitute it with that.
  • So let's do it.
  • So the second equation over here is 10x plus 2.
  • And instead of writing a y there, and I've said it multiple times already, we can write a negative 5x plus 8.
  • The first constraint tells us that's what y is.
  • So negative 5x plus 8 is equal to negative 2.
  • Now, we have one equation with one unknown.
  • We can just solve for x.
  • We have 10x plus.
  • So we can multiply it.
  • We can distribute this 2 onto both of these terms.
  • So we have 2 times negative 5x is negative 10x.
  • And then 2 times 8 is 16.
  • So plus 16 is equal to negative 2.
  • Now we have 10x minus 10x.
  • Those guys cancel out.
  • 10x minus 10x is equal to 0.
  • So these guys cancel out.
  • And we're just left with 16 equals negative 2, which is crazy.
  • We know that 16 does not equal negative 2.
  • This is an inconsistent result.
  • And that's because these two lines actually don't intersect.
  • And we could see that by actually graphing these lines.
  • Whenever you get something like some number equalling some other number that they're clearly not equal to, that means it's an inconsistent result, It's an inconsistent system, and that these lines actually don't intersect.
  • So let me just graph these just to make it clear.
  • This first equation is already in slope y-intercept form.
  • So it looks something like this.
  • That's our x-axis.
  • This is our y-axis.
  • And it's negative 5x plus 8, so 1, 2, 3, 4, 5, 6, 7, 8.
  • And then it has a very steep downward slope.
  • Every time you move forward 1, you have to go down 5.
  • So it looks something like that.
  • That's this first equation right over there.
  • The second equation, let me rewrite it in slope y-intercept form.
  • So it's 10x plus 2y is equal to negative 2.
  • Let's subtract 10x from both sides.
  • You get 2y is equal to negative 10x minus 2.
  • Let's divide both sides by 2.
  • You get y is equal to negative 5x, negative 5x minus 1.
  • So it's y-intercept is negative 1.
  • It's right over there.
  • And it has the same slope as this first line.
  • So it looks like this.
  • It's parallel.
  • It's just shifted down a bit.
  • So it just looks like that.
  • So they're parallel lines.
  • They have the same slope, different y-intercepts.
  • We get an inconsistent result.
  • They don't intersect.
  • And the telltale sign of that, when you're doing it algebraically, is you get something wacky like this.
  • This is why it's called inconsistent.
  • It's not consistent for 16 to be equal to negative 2.
  • These don't intersect.
  • There's no solution to both of these constraints, no x and y that satisfies both of them.