# How do you solve for the x if 8x=y and 2x+y=5?

May 23, 2018

Substitute out $y$ in the second equation and solve for $x$, which is $x = 0.5$

#### Explanation:

The first expression gives us a solution for $y$ in terms of $x$:

$\textcolor{b l u e}{8 x = y}$

We can take this solution and substitute all values of $y$ in equation 2:

$2 x + \textcolor{b l u e}{y} = 5$

$2 x + \textcolor{b l u e}{8 x} = 5$

Because we know $\textcolor{b l u e}{y = 8 x}$ we can make this substitution. Now all that's left is to solve for $x$

$10 x = 5$

$\frac{\cancel{10} x}{\textcolor{red}{\cancel{10}}} = \frac{5}{\textcolor{red}{10}}$

$\textcolor{g r e e n}{x = \frac{1}{2} = 0.5}$