Question

How do you solve the system using elimination `3r - 2s = 1` and `2r - 3s = 9`?

Answer 1

Subtract different multiples of the two equations from one another to eliminate `r` or `s` and find `s = -5` and `r = -3`

Explanation:

First subtract `3` times the second equation from twice the first equation to get:

`-25 = 2(1) - 3(9) = 2(3r-2s)-3(2r-3s) = 5s`

Divide both ends by `5` to get `s = -5`

Secondly, subtract twice the second equation from `3` times the first equation to get:

`-15 = 3(1) - 2(9) = 3(3r-2s)-2(2r-3s) = 5r`

Divide both ends by `5` to get `r = -3`