# How do you solve 9m+n=35 and m-9n=13 using substitution?

##### 1 Answer
Mar 21, 2016

The solution for the system of equations is:
color(blue)(m=4
color(blue)(n=-1

#### Explanation:

$9 m + n = 35$............equation $\left(1\right)$

$m - 9 n = 13$
color(blue)(m =13 + 9n .............equation $\left(2\right)$

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

$9 m + n = 35$

$9 \cdot \left(\textcolor{b l u e}{13 + 9 n}\right) + n = 35$

$\left(9 \cdot 13\right) + \left(9 \cdot 9 n\right) + n = 35$

$117 + 81 n + n = 35$

$82 n = 35 - 117$

$82 n = - 82$

$n = \frac{- 82}{82}$

color(blue)(n=-1

Finding the value of $m$ from equation $\left(2\right)$:

$m = 13 + 9 n$

$m = 13 + 9 \cdot \left(- 1\right)$

$m = 13 - 9$

color(blue)(m=4