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

Jul 4, 2015

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:

$- 25 = 2 \left(1\right) - 3 \left(9\right) = 2 \left(3 r - 2 s\right) - 3 \left(2 r - 3 s\right) = 5 s$

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

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

$- 15 = 3 \left(1\right) - 2 \left(9\right) = 3 \left(3 r - 2 s\right) - 2 \left(2 r - 3 s\right) = 5 r$

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