Question

How do you solve the system using the elimination method for 3x-4y=18 and x+3y=-7?

Answer 1

`(x,y)=(2,-3)`
See below for solution by elimination

Explanation:

Given
[1]`color(white)("XXX")3x-4y=18`
[2]`color(white)("XXX")x+3y=-7`

If we multiply [2] by `3` we can generate an equation with the same `x` coefficient as that in [1]
[3]`color(white)("XXX")3x+9y=-21`

We can now eliminate the `x` term by subtracting [1] from [3]
[4]`color(white)("XXX")13y=-39`

After dividing both sides of [4] by `13`
[5]`color(white)("XXX")y=-3`

Substituting `(-3)` for `y` in [2}
[6]`color(white)("XXX")x+3 * (-3)=-7`

Simplifying
[7]`color(white)("XXX")x-9=-7`

[8]`color(white)("XXX")x=2`