# How do you solve 1/2(x-y) = 2 and 1/2(x+y)+1 = 0?

Apr 14, 2018

$x = 1$ and $y = - 3$

#### Explanation:

Solve like simultaneous equations.

Equation 1: $\frac{1}{2} \left(x - y\right) = 2$
Expand the brackets to get $\frac{1}{2} x - \frac{1}{2} y = 2$

Equation 2: $\frac{1}{2} \left(x + y\right) + 1 = 0$
Expand the brackets to get $\frac{1}{2} x + \frac{1}{2} y + 1 = 0$

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

$\frac{1}{2} x + \frac{1}{2} y + 1 = 0$

Add the two equations together to get
$\frac{1}{2} x + \frac{1}{2} x + \frac{1}{2} y - \frac{1}{2} y + 1 = 2$

$x + 1 = 2$
$x = 1$

Substitute this value of $x$ into either Equation 1 or 2 and solve for $y$

Equation 2: $\frac{1}{2} \left(1\right) + \frac{1}{2} y + 1 = 0$
$\frac{1}{2} + \frac{1}{2} y + 1 = 0$
$\frac{1}{2} y + 1 = - \frac{1}{2}$
$\frac{1}{2} y = - 1$$\frac{1}{2}$
$y = - 3$