# How do you solve the following system using substitution?: -3x + 3y= 3, -5x + y = 13

Oct 26, 2015

$x = - 3$
$y = - 2$

#### Explanation:

First, isolate $y$ in the first equation.

$\textcolor{b l u e}{\left[1\right]} \text{ } - 3 x + 3 y = 3$

$\textcolor{b l u e}{\left[2\right]} \text{ } 3 y = 3 + 3 x$

$\textcolor{b l u e}{\left[3\right]} \text{ } y = 1 + x$

Now substitute the value of $y$ in the first equation to $y$ in the second equation.

$\textcolor{red}{\left[1\right]} \text{ } - 5 x + \textcolor{b l u e}{y} = 13$

$\textcolor{red}{\left[2\right]} \text{ } - 5 x + \textcolor{b l u e}{\left(1 + x\right)} = 13$

$\textcolor{red}{\left[3\right]} \text{ } - 4 x = 12$

$\textcolor{red}{\left[4\right]} \text{ } x = - 3$

Now that we have the value of $x$, we will simply substitute this to the first equation.

$\textcolor{b l u e}{\left[4\right]} \text{ } y = 1 + \left(- 3\right)$

$\textcolor{b l u e}{\left[5\right]} \text{ } y = - 2$