# How do you solve the following system: 4x + y = -1 , 5x - 7y = 12 ?

Apr 13, 2018

$x = \frac{5}{33}$
$y = - \frac{5}{3}$
$\left(\frac{5}{33} , - \frac{5}{3}\right)$

#### Explanation:

$4 x + y = - 1$, $5 x - 7 y = 12$
Take the first equation, $4 x + y = - 1$, and isolate $y$:
$y = - 4 x - 1$. We can substitute this value into the second equation:
$5 x - 7 \left(- 4 x - 1\right) = 12$. Distribute the parentheses:
$5 x + 28 x + 7 = 12$ Combine like terms, isolate $x$ and coeffecient:
$33 x = 5$ Isolate $x$:
$x = \frac{5}{33}$ Input this value into the first equation:
$4 \left(\frac{5}{33}\right) + y = - 1$ Distribute $y$
$\frac{20}{33} + y = - 1$ Isolate $y$
$y = - \frac{55}{33}$
$y = - \frac{5}{3}$