# How do you solve the system of equations: x + 3y = 1 and -2x + y = -23?

Aug 8, 2015

The solution for the system of equations is
color(blue)(x=10, y=-3

#### Explanation:

$x + 3 y = 1$ , multiplying this equation by $2$

$\textcolor{b l u e}{2 x} + 6 y = 2$...............equation $\left(1\right)$

$- \textcolor{b l u e}{2 x} + y = - 23$.....equation $\left(2\right)$

Now , we can solve by elimination , upon addition of the two equations color(blue)(2x gets eliminated.

$\cancel{\textcolor{b l u e}{2 x}} + 6 y = 2$

$- \cancel{\textcolor{b l u e}{2 x}} + y = - 23$

$7 y = - 21$
color(blue)(y=-3

Now, we can find $x$ by substituting the value of $y$ in equation $\left(1\right)$

$x + 3 y = 1$

$x = 1 - 3 y$

$x = 1 - \left(3 \cdot \left(- 3\right)\right)$

color(blue)(x=10