# How do you solve the system 2x+3y=12 and 4x-3y=6?

Jun 11, 2015

If you look, you can see $3 y$ and $- 3 y$ are both present in the equations. That's a good clue to add them together (Elimination).

.......$2 x \cancel{+ 3 y} = 12$
$+$ $4 x \cancel{- 3 y} = 6$

.......$6 x + 0 = 18$

$x = 3$

Then choose one to plug in $x$, and solve for $y$.

$2 \left(3\right) + 3 y = 12$

$6 + 3 y = 12$

$3 y = 6$
$y = 2$

Thus:
$x = 3$
$y = 2$