Question

How do you solve the system of equations: -3x+y=-4 and 2x-y=1?

Answer 1

Add the given equations together to get an equation in terms or just `x`; solve for `x`; then use the solution value in one of the given equations to determine `y`
`(x,y) = (-5, -11)`

Explanation:

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

Adding [1] and [2]
[3]`color(white)("XXXX")` `-x = 5`
Multiplying by `(-1)`
[4]`color(white)("XXXX")` `x = -5`

Substituting `(-5)` for `x` in [1]
[5]`color(white)("XXXX")` `-3(-5) + y = 4`

Simplifying
[6]`color(white)("XXXX")` `y = -11`