# How do you solve 5x + y = 9 and 10x - 7y =-18?

Sep 8, 2015

$\left\{\begin{matrix}x = 1 \\ y = 4\end{matrix}\right.$

#### Explanation:

Take a look at your starting system of equations

$\left\{\begin{matrix}5 x + y = 9 \\ 10 x - 7 y = - 18\end{matrix}\right.$

Notice that if you multiply the first equation by $\left(- 2\right)$, and add the right-hand sides and the left-hand sides of the equations separately, you can eliminate the $x$-term.

This will leave you with one equation with one unknown, $y$.

$\left\{\begin{matrix}5 x + y = 9 | \cdot \left(- 2\right) \\ 10 x - 7 y = - 18\end{matrix}\right.$

$\left\{\begin{matrix}- 10 x - 2 y = - 18 \\ 10 x - 7 y = - 18\end{matrix}\right.$
stackrel("---------------------------------------------------")

$- \textcolor{red}{\cancel{\textcolor{b l a c k}{10 x}}} - 2 y + \textcolor{red}{\cancel{\textcolor{b l a c k}{10 x}}} - 7 y = - 18 + \left(- 18\right)$

$- 9 y = - 36 \implies y = \frac{\left(- 36\right)}{\left(- 9\right)} = \textcolor{g r e e n}{4}$

Now use this value of $y$ in one of the two original equations to find the value of $x$

$5 x + \left(4\right) = 9$

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