# How do solve the following system of equations: -2x + y = 1 and -4x + y = -1?

Oct 9, 2015

I found:
$x = 1$
$y = 3$

#### Explanation:

You can try by multiplying the first equation by $- 1$ and adding the two in columns:
$\left\{\begin{matrix}\textcolor{red}{- 1} \times - 2 x + y = 1 \\ - 4 x + y = - 1\end{matrix}\right.$

$\left\{\begin{matrix}2 x - y = - 1 \\ - 4 x + y = - 1\end{matrix}\right.$ add them:

$- 2 x + 0 = - 2$

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

use this back into the first equation:
$- 2 \cdot 1 + y = 1$
$- 2 + y = 1$
$y = 3$