# How do you solve 4x-3y = -15 and x + y = 5  using substitution?

Feb 11, 2017

x = 0; " "y = 5

#### Explanation:

Given:
$4 x - 3 y = - 15 \textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots} A$
$x + y = 5 \textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} B$

Then, from equation B:
$\textcolor{b l u e}{x = 5 - y}$

Substitute for $x$ in equation A;
$4 \textcolor{b l u e}{\left(5 - y\right)} - 3 y = - 15$
$20 - 4 y - 3 y = - 15$
$20 - 7 y = - 15$
$- 7 y = - 15 - 20 \text{ }$ multiply both sides by $- 1$
$7 y = 35$
$y = 5$

Substitute the value of $y$ in equation B:
$x + y = 5$
$x + 5 = 5$
$x = 5 - 5$
$x = 0$

To check, substitute the values into equation A":
$4 x - 3 y = - 15$
$4 \left(0\right) - 3 \left(5\right) = - 15$
$- 15 = - 15$