Question

How do you solve the following system?: `x + 3-2y=7 , x=-3x + 4y-17`

Answer 1

`(x,y)=(-25/2,-33/4)`

Explanation:

Given
[1]`color(white)("XXX")x+3-2y=7`
[2]`color(white)("XXX")x=-3x+4y-17`

Re-arrange [1] and [2] into standard form to get (respectively)
[3]`color(white)("XXX")x-2y=4`
[4]`color(white)("XXX")4x-4y=-17`

Since this was asked under "Systems Using Substitution"
Re-write [3] as `x` in terms of `y`
[5]`color(white)("XXX")x=2y+4`

Then substitute `(2y+4)` for `x` in [4]
[6]`color(white)("XXX")4(2y+4)-4y=-17`

Simplifying
[7]`color(white)("XXX")8y+16-4y=-17`

[8]`color(white)("XXX")4y=-33`

[9]`color(white)("XXX")y=-33/4`

Substituting `(-33/4)`for `y` in [3]
[10]`color(white)("XXX")x-2(-33/4)=4`

Simplifying
[11]`color(white)("XXX")x+33/2=8/2`

[12]`color(white)("XXX")x=-25/2`

[These values may look a bit ugly, but substituting back into equations [1] and [2] verify that they are correct.]