How do you solve the system of equations -x-y=15 and -8x+8y=24?

1 Answer
Aug 4, 2016

{(x=-9), (y=-6) :}

Explanation:

The system of equations given to you looks like this

{( -color(white)(1)x - color(white)(1)y = 15), (-8x + 8y = 24) :}

Notice that one equation features y with a positive sign and the other has it with a negative sign. This means that if you get the coefficients to match, you can add the two equations and get rid of the y terms.

To do that, multiply the first equation by 8

{( -color(white)(1)x - color(white)(1)y = 15" " | xx 8), (-8x + 8y = 24) :}

this will get you

{ ( -8x - 8y = 120), (-8x + 8y = color(white)(1)24) :}

Now you're ready to add the two equations

{ ( -8x - 8y = 120), (-8x + 8y = color(white)(1)24) :}
color(white)(aaaaaaaaaaaaaaa)/color(white)(a)

-8x + (-8x) - color(red)(cancel(color(black)(8y))) + color(red)(cancel(color(black)(8y))) = 120 + 24

-16x = 144 implies x = 144/(-16) = -9

Take this value of x into the first equation and find the value of y

- (-9) - y = 15

-y = 15 - 9 implies y = -6

Therefore, the two solutions to your system of equations are

{(x=-9), (y=-6) :}