# How do you solve the system of equations \frac { 2} { 3} x - \frac { 1} { 2} y = 3 and \frac { 1} { 3} x - \frac { 1} { 4} y = \frac { 3} { 2}?

Nov 19, 2017

$x = \frac{18 + 3 y}{4}$
OR
$y = \frac{4 x - 18}{3}$

#### Explanation:

$\frac{2}{3} x - \frac{1}{2} y = 3$
$\frac{1}{3} x - \frac{1}{4} y = \frac{3}{2}$

$\implies$

$6 \cdot \left(\frac{2}{3} x - \frac{1}{2} y\right) = 6 \cdot \left(3\right)$
$12 \cdot \left(\frac{1}{3} x - \frac{1}{4} y\right) = 12 \cdot \left(\frac{3}{2}\right)$

$\implies$

$4 x - 3 y = 18$
$4 x - 3 y = 18$

$\implies$

$4 x - 3 y = 18$

$\implies$

$x = \frac{18 + 3 y}{4}$
OR
$y = \frac{4 x - 18}{3}$