# How do you solve 3u + z = 15 and u + 2z = 10?

Sep 7, 2015

$\left\{\begin{matrix}u = 4 \\ z = 3\end{matrix}\right.$

#### Explanation:

Your system of equations looks like this

$\left\{\begin{matrix}3 u + z = 15 \\ u + 2 z = 10\end{matrix}\right.$

Multiply the first equation by $\left(- 2\right)$ to get

$\left\{\begin{matrix}3 u + z = 15 | \cdot \left(- 2\right) \\ u + 2 z = 10\end{matrix}\right.$

$\left\{\begin{matrix}- 6 u - 2 z = - 30 \\ u + 2 z = 10\end{matrix}\right.$

Add these two equations to get one equation with one unknown, $u$

$- 6 u - \textcolor{red}{\cancel{\textcolor{b l a c k}{2 z}}} + u + \textcolor{red}{\cancel{\textcolor{b l a c k}{2 z}}} = - 30 + 10$

$- 5 u = - 20 \implies u = \frac{\left(- 20\right)}{\left(- 5\right)} = \textcolor{g r e e n}{4}$

Now use this value of $u$ in one of the wo original equations to find $z$

$4 + 2 z = 10$

$2 x = 6 \implies z = \frac{6}{2} = \textcolor{g r e e n}{3}$