# How do you solve the following system of equations? 3x +4y = 15, 3x + 2y = 12

Mar 14, 2018

$\left(3 , \frac{3}{2}\right)$

#### Explanation:

Because we have a $3 x$ in both equations, we can solve this system using the elimination method.

$3 x + 4 y = 15$
$3 x + 2 y = 12$

You can subtract the bottom equation from the top one to get:

$2 y = 3$
$y = \frac{3}{2}$

To solve for $x$, you can plug $y$ into one of the equations. In this case, the bottom equation would be easier to use.

$3 x + 2 \left(\frac{3}{2}\right) = 12$
$3 x + 3 = 12$
$3 x = 9$
$x = 3$

$x = 3$ and $y = \frac{3}{2}$, so the solution to this system is...
$\left(3 , \frac{3}{2}\right)$