# How do you solve the system 1/2x + 3/4y = -1/4 and 3/4x + -1/4y = 1?

Jun 13, 2018

$x = 1$ and $y = - 1$

#### Explanation:

$\frac{1}{2} x + \frac{3}{4} y = - \frac{1}{4}$
Multiply all by 4
$2 x + 3 y = - 1$

$\frac{3}{4} x + - \frac{1}{4} y = 1$
$\frac{3}{4} x - \frac{1}{4} y = 1$
Multiply all by 4
$3 x - y = 4$
$y = 3 x - 4$

Substitute $y$ into the equation
$2 x + 3 \left(3 x - 4\right) = - 1$
$2 x + 9 x - 12 = - 1$
$11 x = 11$
$x = 1$

Substitute $x$ into the equation
$y = 3 \left(1\right) - 4$
$y = 3 - 4$
$y = - 1$