# How do you solve the system of equations: y=3x+8 and y=4x+5?

Aug 6, 2015

$\left\{\begin{matrix}x = 3 \\ y = 17\end{matrix}\right.$

#### Explanation:

All you have to do in order to solve this system of equations is use the value of $y$ that you get from one equation into the other equation.

In your case, you know that

$y = 3 x + 8$

and that

$y = 4 x + 5$

This automatically implies that

$3 x + 8 = 4 x + 5$

Solve this equation for $x$, then take thevalue of $x$ and use it to find $y$

$4 x - 3 x = 8 - 5 \implies x = \textcolor{g r e e n}{3}$

This means that $y$ will be

$y = 3 \cdot \left(3\right) + 8 = \textcolor{g r e e n}{17}$