How do you solve 8m + n = 34 and m - 4n = 29 using substitution?

Apr 18, 2016

The solution for the system of equations is:
color(blue)(m=5
 color(blue)(n = - 6

Explanation:

$8 m + n = 34$..............equation $\left(1\right)$

$m - 4 n = 29$
color(green)(m = 29 + 4n ..............equation $\left(2\right)$

Substituting equation $2$ in $1$

$8 m + n = 34$

$8 \cdot \left(\textcolor{g r e e n}{29 + 4 n}\right) + n = 34$

$232 + 32 n + n = 34$

$33 n = 34 - 232$

$33 n = - 198$

$n = - \frac{198}{33}$

 color(blue)(n = - 6

Finding $m$ from equation $1$:
$8 m + n = 34$

$8 m = 34 - n$

$8 m = 34 - \left(- 6\right)$

$8 m = 34 + 6$

$8 m = 40$

$m = \frac{40}{8}$

color(blue)(m=5