# How do you solve the system of equations: x - 2y = -1, 2x - y = 4?

Aug 14, 2015

The solutions are:
color(blue)(x=3,y=2

#### Explanation:

$x - 2 y = - 1$ , multiplying this equation by $2$
$\textcolor{b l u e}{2 x} - 4 y = - 2$ ....equation $\left(1\right)$

$\textcolor{b l u e}{2 x} - y = 4$.........equation $\left(2\right)$

Now we can solve through elimination as we have the term $\textcolor{b l u e}{2 x}$ common to both equations:

Subtracting equation $2$ from $1$

$\cancel{\textcolor{b l u e}{2 x}} - 4 y = - 2$
$- \cancel{\textcolor{b l u e}{2 x}} + y = - 4$

$- 3 y = - 6$
color(blue)(y=2

Now we find $x$ by substituting $y$ in equation $1$
$x - 2 y = - 1$
$x = - 1 + 2 y$
$x = - 1 + 2 \cdot \left(2\right)$
$x = - 1 + 4$
color(blue)(x=3