# How do you solve 5m+n=39 and m-3n=27 using substitution?

Mar 28, 2016

The solution for the system of equations is:
color(green)(m = 9
$\textcolor{g r e e n}{n = - 6}$

#### Explanation:

$5 m + n = 39$..................equation $\left(1\right)$

$m - 3 n = 27$
color(green)(m = 27 + 3n ..................equation $\left(2\right)$

Substituting equation $\left(2\right)$ in $\left(1\right)$

$5 m + n = 39$

$5 \cdot \left(\textcolor{g r e e n}{27 + 3 n}\right) + n = 39$

$5 \cdot \left(\textcolor{g r e e n}{27}\right) + 5 \cdot \textcolor{g r e e n}{\left(3 n\right)} + n = 39$

$135 + 15 n + n = 39$

$135 + 16 n = 39$

$16 n = - 96$

$n = - \frac{96}{16}$

$\textcolor{g r e e n}{n = - 6}$

Finding $m$ by substituting the value of $n$ in equation $\left(2\right)$:
$m = 27 + 3 n$

$m = 27 + 3 \cdot \left(- 6\right)$

$m = 27 - 18$

color(green)(m = 9