Question

How do you solve the system using the elimination method for 9x - 9y = 27 and 7y - 3x = -11?

Answer 1

`(x,y) = (5/2, -1/2)`

Explanation:

[1]`color(white)("XXXX")` `9x-9y=27`
[2]`color(white)("XXXX")` `7y-3x = -11`

Resequence the terms of [2] so the variables occur in the same order as in [1]
[3]`color(white)("XXXX")` `-3x+7y = -11`

Multiply [3] by `3`
[4]`color(white)("XXXX")` `-9x+21y = -33`

Add [1] and [4]
[5]`color(white)("XXXX")` `12y = -6`

Divide [5] by`12`
[6]`color(white)("XXXX")` `y = -1/2`

Substitute `y=-1/2` into [1]
[7]`color(white)("XXXX")` `9x-9(-1/2) = 27`

Simplifying
[8]`color(white)("XXXX")` `9x = 45/2`

[9]`color(white)("XXXX")` `x = 5/2`