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

Jun 26, 2018

Using substitution, we can find that $x = 1$ and $y = - \frac{5}{2}$.

#### Explanation:

Let's solve the second equation for one variable. We'll choose $x$ first:

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

Let's now plug that into our first equation:

$\frac{3}{4} \left(- \frac{3}{2} - y\right) - \frac{1}{2} y = - \frac{1}{2}$
$- \frac{9}{8} - \frac{3}{4} y - \frac{1}{2} y = - \frac{1}{2}$
$- \frac{9}{8} - \frac{3}{4} y - \frac{2}{4} y = - \frac{1}{2}$
$- \frac{9}{8} - \frac{1}{4} y = - \frac{1}{2}$
$- \frac{1}{4} y = - \frac{1}{2} + \frac{9}{8}$
$- \frac{1}{4} y = - \frac{4}{8} + \frac{9}{8}$
$\frac{- \frac{1}{4} y}{- \frac{1}{4}} = \frac{\frac{5}{8}}{- \frac{1}{4}}$
$y = - \frac{5}{2}$

Let's now take our y-value and put that into our equations solved for $x$:

$x = - \frac{3}{2} - \left(- \frac{5}{2}\right)$
$x = - \frac{3}{2} + \frac{5}{2} = \frac{2}{2} = 1$

Hope this helped!