Question

How do you solve the following system?: `-9x - 3y = 2 , 3x – y = -1`

Answer 1

`color(green)(x=-5/18, y= 1/6)`

Explanation:

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

Multiplying [2] by `3`
`color(white)("XXXX")3xx(3x-y)=3xx(-1)`
[3]`color(white)("XXX")9x-3y=-3`

Adding [1] and [3]
`color(white)("XXXX")-9x-3y=2`
`color(white)("XXXXX")underline(9x-3y)=underline(-3)`
[4]`color(white)("XXXXXX")-6y=-1`

Dividing [4] by `(-6)`
`color(white)("XXX")(cancel(-6)y)/cancel(-6)=(cancel(-)1)/(cancel(-)6)`
[5]`color(white)("XXX")y=1/6`

Substituting `(1/6)` for `y` in [2]
[6]`color(white)("XXX")3x-(1/6)=-1`

Adding `1/6` to both sides of [6]
`color(white)("XXX")3xcancel(-(1/6))cancel(+1/6)=-1+1/6`

[7]`color(white)("XXX")3x=-5/6`

Dividing both sides of [7] by `3`
`color(white)("XXX")(cancel(3)x)/cancel(3)= -(5/6)/3`

[8]`color(white)("XXX")x=-5/18`