# How do you solve the following system?: y=2x + 3 , x + 3y = -3

Dec 24, 2015

$\left(- \frac{12}{7} , - \frac{3}{7}\right)$

#### Explanation:

You can solve this system of equation by substitution

color(red)(y = 2x +3
$x + 3 y = - 3$

Substitute $y = 2 x + 3$ into the second equation

$x + 3 \left(\textcolor{red}{2 x + 3}\right) = - 3$

Distribute and combine like terms

$x + 6 x + 9 = - 3$

$7 x + 9 = - 3$
$7 x = - 3 - 9$

$7 x = - 12$

$x = - \frac{12}{7}$

Then re-substitute $x = - \frac{12}{7}$ into $y = 2 x + 3$ to solve for $y$

$y = 2 \left(- \frac{12}{7}\right) + 3$
$\implies y = - \frac{24}{7} + \frac{21}{7}$
$\implies y = - \frac{3}{7}$