Question

How do you solve the system `4x-y=9` and `x-3y=16`?

Answer 1

`(x,y)=(1,-5)`

Explanation:

Given
[1]`color(white)("XXXX")` `4x-y = 9`
[2]`color(white)("XXXX")` `x-3y = 16`

Re-arrange the terms of [2] to get
[3]`color(white)("XXXX")` `x = 3y+16`

Using [3] substitute `(3y+16)` for `x` in [1]
[4]`color(white)("XXXX")` `4(3y+16)-y = 9`

Simplifying
[5]`color(white)("XXXX")` `11y +64 = 9`
[6]`color(white)("XXXX")` `11y = -55`
[7]`color(white)("XXXX")` `y = -5`

Using [7] substitute `(-5)` for `y` in [1]
[8]`color(white)("XXXX")` `4x - (-5) = 9`
[9]`color(white)("XXXX")` `4x = 4`
[10]`color(white)("XXXX")` `x = 1`

`(x,y) = (1,-5)`