# How do you solve x + 5y - 10 = 0 and x = 2y - 8 using substitution?

Mar 18, 2018

$y = \frac{18}{7} , x = - \frac{34}{7}$

#### Explanation:

We have two equations in two variables. In these situations, our goal should be to get one equation in one variable, solve for that variable, and finally, use the value of that variable to find the second unknown variable.

Our second equation, $x = 2 y - 8 ,$ tells us that for our first equation, we can replace all instances of $x$ with $2 y - 8$ since these two expressions are equal. Doing so yields

$x + 5 y - 10 = 0 \Leftrightarrow 2 y - 8 + 5 y - 10 = 0$

We now have one equation in one variable, $y .$ We can then solve for $y$:

$2 y - 8 + 5 y - 10 = 0$

$7 y - 18 = 0$
$7 y = 18$
$y = \frac{18}{7}$

We can plug $y = \frac{18}{7}$ into $x = 2 y - 8$ to solve directly for $x :$

$x = 2 \left(\frac{18}{7}\right) - 10$
$x = \frac{36}{7} - 10 = \frac{36}{7} - \frac{70}{7} = - \frac{34}{7}$