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# Solutions to 2-variable equations

CCSS.Math:

## Video transcript

which of the ordered pairs is a solution of the following equation negative 3x minus y is equal to 6 well we have to remind ourselves is when we're given an ordered pair the first number is the x-coordinate and the second number is the y coordinate or the y-value so when they tell us the ordered pair negative 4 comma 4 they're saying hey look if x is equal to negative 4 and y is equal to positive 4 does that satisfy this equation and what we can do is we can just try that out so we have negative 3 and everywhere where we see an X everywhere we see an X we can replace it with negative 4 so it's negative 3 times negative 4 minus - and everywhere we see and everywhere we see ay and everywhere we see a Y we can replace it with positive 4 we replace it with positive 4 so negative 3 times X minus y which is 4 needs to be equal to 6 needs to be equal to 6 now is this indeed the case negative 3 times negative 4 is positive 12 positive 12 minus 4 positive 12 minus 4 is equal to 8 it's not equal to 6 is not equal it is not equal to 6 so this one does not work out so let's see negative 3 comma 3 so we can do the same thing here let's see what happens when X is equal to negative 3 and Y is equal to positive 3 so we substitute back in we get negative 3 negative 3 times X which now we're going to try out X being equal to negative 3 minus y minus y Y is positive 3 here - y let me do that Y color that blue minus y now needs to be equal to now needs to be equal just like before it needs to be equal to 6 so negative 3 times negative 3 that's going to be positive nine nine minus three is indeed equal to six nine minus three is indeed equal to six nine minus three 6 that is equal to six this works out so negative 3 comma 3 is an ordered pair that is a solution to this equation