Question

How do you solve 2x - 5y = 11 and 4x + 10y = 18?

Answer 1

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

Explanation:

[1]`color(white)("XXX")2x-5y=11`
[2]`color(white)("XXX")4x+10y=18`

Multiply [1] by `2`
[3]`color(white)("XXX")4x-10y=22`

Subtract [3] from [2]
[4]`color(white)("XXX")20y = -4`

Divide [4] by `20`
[5]`color(white)("XXX")y = -1/5`

Substitute `(-1/5)` for `y` in [1]
[6]`color(white)("XXX")2x-5(-1/5)=11`

Simplify
[7]`color(white)("XXX")2x+1=11`

Subtract `1`
[8]`color(white)("XXX")2x=10`

Divide by `2`
[9]`color(white)("XXX")x=5`