Question

How do you solve the following system?: `-13x -3y =6, 8x -y = -1`

Answer 1

`(x,y) = (-9/37,35/37)`
(see below for method of solution)

Explanation:

Given
[1]`color(white)("XXX")-13x-3y=6`
[2]`color(white)("XXX")8x-y=-1`

Multiply [2] by 3 (to give `y` the same coefficient as in [1])
[3]`color(white)("XXX")24x-3y=-3`

Subtract [1] from [3] (to get rid of the `y` term)
[4]`color(white)("XXX")37x=-9`

Divide [4] by 27
[5]`color(white)("XXX")x=-9/37`

Re-write [2] as an equation for `y` by adding `(y+1)` to both sides and switching the sides
[6]`color(white)("XXX")y=8x+1`

Substitute `(9/37)` from [5] for `x` in [6]
[7]`color(white)("XXX")y=8(-9/37)+1`

Simplify [7]:
[8]`color(white)("XXX")y=-35/37`

Probably the biggest problem here is trusting your calculations (or being willing to do them in the first place) since the answer isn't "pretty".

If it helps a graph can help verify that the answer is within an appropriate range:
graph{(-13x-3y-6)*(8x-y+1)=0 [-3.97, 3.826, -2.976, 0.917]}