Question

How do solve the following linear system?: `-9x + 6y = -2 , 3x-y=7`?

Answer 1

`(x,y)=(40/9,19/3)`

Explanation:

Given
[1]`color(white)("XXX")-9x+6y=-2`
[2]`color(white)("XXX")3x-y=7`

Multiplying [2] by `3`
[3]`color(white)("XXX")9x-3y=21`

Adding [1] and [3]
[4]`color(white)("XXX")3y=19`

Dividing [4] by `3`
[5]`color(white)("XXX")y=19/3`

Substituting `19/4` for `y` in [2]
[6]`color(white)("XXX")3x-19/3=7`

Adding `19/4` to both sides of [6] and simplifying the right side
[7]`color(white)("XXX")3x=40/3`

Dividing [7] by `3`
[8]`color(white)("XXX")x=40/9`

You might want to simplify this as `(x,y)=(3 4/9,6 1/3)`
however
leaving these values in their improper fraction forms will probably make the verification easier (...and you always do this; right?)