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

Mar 30, 2015

Simplify your equations by multiplying both sides by a constant to clear the fractions then solve as normal.

$\left(\frac{3}{4}\right) x - \left(\frac{1}{2}\right) y = - \left(\frac{1}{2}\right)$ multiplied by $4$ becomes
$3 x - 2 y = - 2$

$x + y = - \left(\frac{3}{2}\right)$ multiplied by $2$ becomes
$2 x + 2 y = - 3$

Adding these modified equations together gives
$5 x = - 5$

So
$x = - 1$
and by substitution back into any one of the prior equations
$y = - \frac{1}{2}$