# How do you solve 2x+7y=10 and x-2y=15?

Aug 5, 2015

$\left\{\begin{matrix}x = \frac{125}{11} \\ y = - \frac{20}{11}\end{matrix}\right.$

#### Explanation:

You could solve this sytem of equations by multiplication.

More specifically, you can multiply the second equation by $- 2$ to get

$- 2 \cdot \left(x - 2 y\right) = - 2 \cdot 15$

$- 2 x + 4 y = - 30$

The two equations now look like this

$\left\{\begin{matrix}2 x + 7 y = 10 \\ - 2 x + 4 y = - 30\end{matrix}\right.$

Next, add the left side and the right side of the equations separately to cancel out the $x$-term

$\textcolor{red}{\cancel{\textcolor{b l a c k}{2 x}}} + 7 y - \textcolor{red}{\cancel{\textcolor{b l a c k}{2 x}}} + 4 y = 10 + \left(- 30\right)$

$11 y = - 20 \implies y = \textcolor{g r e e n}{- \frac{20}{11}}$

Now take this value of $y$ and use it in the first equation to find the value of $x$

$2 x + 7 \cdot \frac{- 20}{11} = 10$

$2 x = 10 + \frac{140}{11}$

$2 x = \frac{250}{11} \implies x = \frac{250}{11} \cdot \frac{1}{2} = \textcolor{g r e e n}{\frac{125}{11}}$