# How do you solve 9m+n=20 and m-4n=31 using substitution?

May 9, 2018

color(blue)(m = 15, n = -4

#### Explanation:

$9 m + n = 20 , \text{ Eqn (1)}$

$m - 4 n = 31 , \text{ Eqn (2)}$

$m = 31 + 4 n$

Substituting value of m in terms of n in Eqn 91),

$9 \cdot \left(31 + 4 n\right) + n = 20$

$279 + 36 n + n = 20$

$37 n = - 259$

color(blue)(n = -259/37 = -4

Substituting value of n in Eqn (2),

$m - 4 \cdot - 4 = 31$

color(blue)(m = 31 - 16 = 15