Question

How do you determine the solution in terms of a system of linear equations for `x + 3y = -3`, `x - 4y = 11`?

Answer 1

`(x,y) = (3,-2)`

Explanation:

Given
[1]`color(white)("XXX")x+3y=-3`
[2]`color(white)("XXX")x-4y=11`

Subtract [2] from [1]
[3]`color(white)("XXX")7y=-14`

Divide both sides of [3] by `7`
[4]`color(white)("XXX")y=-2`

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

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

[7]`color(white)("XXX")x=3`

Recommendation: verify by plugging `(3,-2)` for (`x,y)` back into the original equations.