Question

How do you solve `-5x + 14y = 16 ; -3x + 9y = 12`?

Answer 1

`(x,y)=(8,4)`

Explanation:

Given
[1]`color(white)("XXX")-5x+14y=16`
[2]`color(white)("XXX")-3x+9y=12`

Multiply each equation by a constant to make coefficients of `x` inverse of each other.
[2]=[1]`xx(-3)` `color(white)("XXX")15x-42y=-48`
[3]=[2]`xx5` `color(white)("XXXxx")-15x+49y=color(white)("XX")60`

Add [2] and [3] to get rid of `x` term
[4]`color(white)("XXXXXXXXXXXXXX")7y=28`

Divide both sides of [4] by `7`
[5]`color(white)("XXXXXXXXXXXXXXX")y=4`

Substitute `4` in place of `y` in [2] (we could have used [1])
[6]`color(white)("XXX")-3x+9 * 4 = 12`

Simplifying
[7]`color(white)("XXX")-3x+36=12`

[8]`color(white)("XXX")-3x=-24`

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