# How do you solve the system of equations 3x + 7y = - 3 and x + \frac { 7} { 4} y = - \frac { 2} { 3}?

Nov 22, 2016

$x = \frac{1}{3}$
$y = - \frac{4}{7}$

#### Explanation:

$3 x + 7 y = - 3$

$x + \frac{7}{4} y = \frac{2}{- 3}$
Multiply everything by $- 3$:
$- 3 \left(x + \frac{7}{4} y\right) = - 3 \left(\frac{2}{- 3}\right)$
$- 3 x - \frac{21}{4} y = 2$

Add the 2 equations (elimination):
$3 x + 7 y = - 3$
$- 3 x - 5.25 y = 2$

$1.75 y = - 1$
$y = \frac{1}{- \frac{7}{4}}$
$y = - \frac{4}{7}$

Substitute $y = - \frac{4}{7}$ into one of the original equations:
$x + \frac{7}{4} \left(- \frac{4}{7}\right) = - \frac{2}{3}$
$x - 1 = - \frac{2}{3}$
$x = \frac{1}{3}$