Question

How do you solve `5x + 4y = 6` and `-2x - 3y = -1`?

Answer 1

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

Explanation:

[1]`color(white)("XXXX")` `5x+4y=6`
[2]`color(white)("XXXX")` `-2x-3y=-1`

Multiply [1] by 2 and [2] by `(-5)` to get 2 equations with identical coefficients for `x`
[3]`color(white)("XXXX")` `10x+8y = 12`
[4]`color(white)("XXXX")` `10x+15y=5`

Subtract [4] from [3]
[5]`color(white)("XXXX")` `-7y = 7`

Divide both sides by `(-7)`
[6]`color(white)("XXXX")` `y = -1`

Substitute `(-1)` for `y` in [1]
[7]`color(white)("XXXX")` `5x+4(-1) = 6`

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