# What is the solution of the system? 5x+4y=-2 and x-4y=14

May 21, 2018

$\left(28 \frac{1}{3} , 2 \frac{5}{6}\right)$

#### Explanation:

We can make the second equation
$x = 4 y + 14$
Substituting that value into the first equation, we get
$5 \cdot \left(4 y + 14\right) + 4 y = - 2$
$24 y = 68$
$y = \frac{17}{6}$, or $2 \frac{5}{6}$
Substituting this value of $y$ into either equation, we solve for $x$ as $\frac{85}{3}$, or $28 \frac{1}{3}$

This gives us the solution $\left(28 \frac{1}{3} , 2 \frac{5}{6}\right)$