Question

How do you solve the following linear system: `4x + 5y = -3 , -x + y = 3`?

Replaced a `+` with `=` for the first equation; hopefully, this is what was intended.

Answer 1

`x=-2`, `y=-1`.

Explanation:

From the second equation, we know that `y=3+x`.

So, the first equation becomes

`4x+5color(green)(y)=-3 -> 4x+5color(green)((3+x))=-3`

Expand the left memeber: `4x+15+5x = 9x+15`

So, `9x+15=-3 \iff 9x = -18 iff x=-2`

Knowing this, we obtain `y`, since `y=3+x=3-2=1`

Answer 2

`(x,y)=(-2,1)`

Explanation:

Given
[1]`color(white)("XXX")4x+5y=-3`
[2]`color(white)("XXX")-x+y=3`

Multiply [2] by `4`
[3]`color(white)("XXX")-4x+4y=12`

Add [1] and [3]
[4]`color(white)("XXX")9y=9`

Divide [4] by `9`
[5]`color(white)("XXX")y=1`

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

Subtract `1` from both sides of [6]
[7]`color(white)("XXX")-x=2`

Multiply both sides of [7] by `(-1)`
[8]`color(white)("XXX")x=-2`