Question

How do you solve the system of equations `x+ 3y = 21` and `-x + 8y = 23`?

Answer 1

`x = 9 and y = 4`

Explanation:

This is absolutely the BEST scenario you could wish for!
You have additive inverses as the first term in each equation!
Simply adding the equations together will eliminate the `x-`terms.

`color(white)(xxxxxx)x+3y = 21` ........................A
`color(white)(xxxx)-x+8y = 23` ........................B
`A+B:" "11y = 44`
`color(white)(xxxxxxxxxx)y = 4`

Now substitute this value for y in one of the equations:

`y=4 " in " A: x+3(4) = 21`
`color(white)(xxxxxxxxx)x+12 = 21`
`color(white)(xxxxxxxxxxxxx)x = 21-12`
`color(white)(xxxxxxxxxxxxx)x = 9`