# How do you solve m+2n=1 and 5m+3n= -23?

May 11, 2018

n = -4, m = 9

#### Explanation:

$m + 2 n = 1$
$5 m + 3 n = - 23$

This is a system of equations, and the best way to solve this one is through substitution. Basically, we're going to isolate for 1 variable and plug it into the second question to get both variables.

$m + 2 n = 1$

Let's find m. Subtract 2n from both sides. You should get:

$m = - 2 n + 1$

Now that we know what $m$ is, we can plug it into our second equation:

$5 \left(- 2 n + 1\right) + 3 n = - 23$

Distribute.

$- 10 n + 5 + 3 n = - 23$

Combine like terms.

$7 n + 5 = - 23$

Subtract 5 from both sides.

$7 n = - 28$

Divide by 7 to isolate for n.

$n = - 4$

Now, plug this back into the first equation:

$m = - 2 n + 1$
$m = - 2 \left(- 4\right) + 1$

Multiply.

$m$ = 8 + 1
$m$ = 9