# How do you solve the system of equations 5x+2y=75, -x-2y=-31?

Dec 10, 2016

$x = 11$ and $y = 10$

#### Explanation:

Step 1) Solve the second equation for $x$:

$- x + x - 2 y + 31 = - 31 + 31 + x$

$- 2 y + 31 = x$

$x = - 2 y + 31$

Step 2) Substitute $- 2 y + 31$ into the first equation for $x$ and then solve for $y$:

$5 \left(- 2 y + 31\right) + 2 y = 75$

$- 10 y + 155 + 2 y = 75$

$8 y + 155 = 75$

$8 y + 155 - 155 = 75 - 155$

$8 y = - 80$

$\frac{8 y}{8} = \frac{80}{8}$

$y = 10$

Step 3) Substitute $10$ for $y$ into the solution for the second equation and the end of Step 1).

$x = - 2 \cdot 10 + 31$

$x = - 20 + 31$

$x = 11$