# How do you solve x + y/3 = 4 and x/4 - y = 6?

Jul 17, 2015

$x = \frac{72}{13} , y = - \frac{60}{13}$

#### Explanation:

Step 1: Make $y$ the subject of one of the equations:
$x + \frac{y}{3} = 4$ => $y = 12 - 3 x$

Step 2: Substitute this into the other equation and solve for $x$:
$\frac{x}{4} - y = \frac{x}{4} - 12 + 3 x = 6$ => $x - 48 + 12 x = 24$
=> $x = \frac{72}{13}$

Step 3: Use this value in one of the equations and solve for $y$:
$x + \frac{y}{3} = \frac{72}{13} + \frac{y}{3} = 4$ => $\frac{y}{3} = \frac{52}{13} - \frac{72}{13} = - \frac{20}{13}$
=> $y = - \frac{60}{13}$