Question

How do you solve the following system?: `15x +57y =62, 3x -y = -2`

Answer 1

`(x,y)=(26/93,36/31)`

Explanation:

Given:
[1]`color(white)("XXX")15x+57y=62`
[2]`color(white)("XXX")3x-y=-2`

Multiply [2] by 5
[3]`color(white)("XXX")15x-5y=-10`

Subtract [3] from [1]
[4]`color(white)("XXX")62y=72`

Divide [4] by 62
[5]`color(white)("XXX")y=36/31`

Substitute `36/31` for `y` in [2]
[6]`color(white)("XXX")3x-36/31=-2`

Add `36/31` to both sides of [6]
[7]`color(white)("XXX")3x= -26/31`

Divide [7] by 3
[8]`color(white)("XXX")-26/93`