Question

How do solve the following linear system?: `1/3x + 3y = 9 , 8x + 3y= -9`?

Answer 1

You can solve it either using substitution or elimination, but the following proof will use substitution.

Explanation:

`1/3x` + 3y = 9
3y = 9 - `1/3x`
y = 3 - `1/9x`
8x + 3(3 - `1/9x`) = -9
8x + 9 - `1/3x` = -9
`23/3x` + 9 = -9
`23/3x` = -18
23 = -54x
`-54/23` = x
8(`-54/23`) + 3y = -9
`-432/23` + 3y = -9
`-432/23` + 9 = -3y
`-225/23` = -3y
`75/23` = y

The solution set is (`-54/23`, `75/23`)