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

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Answer 1 · 2016-03-21T17:02:19

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

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

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

Substituting equation $(2)$ $(2)$ in $(1)$ $(1)$

$9 m + n = 35$ $9m + n =35$

$9 \cdot (13 + 9 n) + n = 35$ $9 * (color(blue)(13 + 9n )) + n =35$

$(9 \cdot 13) + (9 \cdot 9 n) + n = 35$ $(9 * 13) + (9 * 9n) + n =35$

$117 + 81 n + n = 35$ $117 + 81n + n =35$

$82 n = 35 - 117$ $82n =35- 117$

$82 n = - 82$ $82n =- 82$

$n = \frac{- 82}{82}$ $n = (-82) / 82$

$n = - 1$ $color(blue)(n=-1$

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

$m = 13 + 9 n$ $m =13 + 9n$

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

$m = 13 - 9$ $m =13 - 9$

$m = 4$ $color(blue)(m=4$

How do you solve 9m+n=359m+n=359m+n=35 and m-9n=13m−9n=13m-9n=13 using substitution?