Question

How do you solve `6x + 5y = -12` and `-9x + y = 69` using substitution?

Answer 1

`(x,y)=color(blue)(""(-7,6))`

Explanation:

Given
[1]`color(white)("XXX")6x+5y=-12`
[2]`color(white)("XXX")-9x+y=69`

re-arranging [1]
[3]`color(white)("XXX")y=9x+69`

substituting `(9x+69)` from [3] for `y` in [1]
[4]`color(white)("XXX")6x+5(9x+69)=-12`

simplifying
[5]`color(white)("XXX")51x+345=-12`

[6]`color(white)("XXX")51x=-357`

[7]`color(white)("XXX")x=-7`

substituting `(-7)` for `x` in [3]
[8]`color(white)("XXX")y=9*(-7)+69=6`