# How do you solve the system 2x+5y=38 and x-3y=-3 using substitution?

Aug 23, 2017

$x = 9$

$y = 4$

#### Explanation:

First, let's take the second equation and rearrange it to make $x$ the subject:

$x - 3 y = - 3 \to x = 3 y - 3$

Insert the rearranged equation in the first equation, in place of $x$:

$2 \left(3 y - 3\right) + 5 y = 38$

Now calculate $y$:

$6 y - 6 + 5 y = 38$

$11 y = 44$

$y = 4$

Now substitute the value of $y$ into the rearranged equation to find $x$:

$x = 3 \left(4\right) - 3$

$x = 12 - 3 \to x = 9$