Question

How do you solve `3x + y = 2` and `4x + y = 20` using substitution?

Answer 1

`(x,y)=(18,-52)`

Explanation:

Given
[1]`color(white)("XXX")3x+y=2`
[2]`color(white)("XXX")4x+y=20`

We can re-arrange [1] into the form:
[3]`color(white)("XXX")y=2-3x`

Then we can substitute (as requested) `(2-3x)` for `y` in [2]
[4]`color(white)("XXX")4x+(2-3x)=20`

Simplifying [4]
[5]`color(white)("XXX")x+2=20`

The subtracting `2` from both sides of [5]
[6]`color(white)("XXX")x=18`

Based on [6], we can now substitute `18` for `x` in [1]
[7]`color(white)("XXX")3 * 18 +y=2`

With some simplification
[8]`color(white)("XXX")54+y=2`

[9]`color(white)("XXX")y=-52`