# How do you solve -10x + y = 0 and 5x + 3y = -7?

Sep 6, 2015

$\left\{\begin{matrix}x = - \frac{1}{5} \\ y = - 2\end{matrix}\right.$

#### Explanation:

Your starting system of equations looks like this

$\left\{\begin{matrix}- 10 x + y = 0 \\ 5 x + 3 y = - 7\end{matrix}\right.$

Multiply the second equation by $2$ to get

$\left\{\begin{matrix}- 10 x + y = 0 \\ 10 x + 6 y = - 14\end{matrix}\right.$

If you add these equations by adding the left-hand side and the right-hand side separately, you can eliminate the $x$-term.

The resulting equation will only have one unknown, $y$.

$\left\{\begin{matrix}- 10 x + y = 0 \\ 10 x + 6 y = - 14\end{matrix}\right.$
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$- \textcolor{red}{\cancel{\textcolor{b l a c k}{10 x}}} + y + \textcolor{red}{\cancel{\textcolor{b l a c k}{10 x}}} + 6 y = 0 + \left(- 14\right)$

$7 y = - 14 \implies y = \frac{- 14}{7} = \textcolor{g r e e n}{- 2}$

Pick one of the original equations and substitute $y$ with the value you've just calculated to get the value of $x$

$- 10 x + \left(- 2\right) = 0$

$- 10 x = 2 \implies x = \textcolor{g r e e n}{- \frac{1}{5}}$