# How do you solve the following system?:  -x+5y=7 , x=-2y+1

Nov 14, 2015

Use linear combination or substitution.

#### Explanation:

$- x + 5 y = 7$
$+ \left(x + 2 y = 1\right)$
$\textcolor{red}{0 x + 7 y = 8}$
Therefore, $7 y = 8$ and $y = \frac{8}{7}$. From here, plug $\frac{8}{7}$ in for $y$ in either equation and solve for $x$.

Another option would be substitution, since from the second equation you know that $x = - 2 y + 1$, would be to replace $x$ with $- 2 y + 1$ in the equation $- x + 5 y = 7$.

This would give: $- \left(- 2 y + 1\right) + 5 y = 7$
$2 y - 1 + 5 y = 7$
$7 y - 1 + 7$
$7 y = 8$
Again, we see that $\textcolor{b l u e}{y = \frac{8}{7}}$ and we would use that value to determine that $\textcolor{b l u e}{x = - \frac{9}{7}}$.