# How do you solve the system using the elimination method for 3/2x - 2/3y =3 and 1/2x - 1/4y= -1?

Jul 15, 2015

I found:
$x = 34$
$y = 72$

#### Explanation:

I would multiply the second equation by $- 3$ to get:
{3/2x-2/3y=3
{color(red)(-3/2x+3/4y=3)
adding the two equations (in columns) you get:
$0 - \frac{2}{3} y + \frac{3}{4} y = 6$
$\frac{- 8 y + 9 y}{12} = 6$ and rearranging:
$y = 6 \cdot 12 = 72$
substituting back $y = 72$ into the first equation you get:
$\frac{3}{2} x - \frac{2}{3} \cdot 72 = 3$
$\frac{3}{2} x - 48 = 3$
$\frac{3}{2} x = 51$
and $x = 34$