Question

How do you solve `y = 5x - 10` and `y = 3x + 8` using substitution?

Answer 1

`(x,y)=(9,35)`
(see below for methodology)

Explanation:

Given
[1]`color(white)("XXX")y=5x-10`
[2]`color(white)("XXX")y=3x+8`

Using [1] we can substitute `5x-10` for `y` in [2]
[3]`color(white)("XXX")5x-10=3x+8`

Simplifying:
[4]`color(white)("XXX")2x=18`

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

We can now use [5] to substitute `9` for `x` in [1]
[6]`color(white)("XXX")y=5 * (9)-10`

Simplifying
[7]`color(white)("XXX")y=35`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We could (and should) verify this result by substituting
`x=9` and `y=35` in [2]
`color(white)("XXX")35 = 3 * (9) + 8` (correct)