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

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Answer 1 · 2016-03-28T16:42:15

The solution for the system of equations is:
$m = 9$ $color(green)(m = 9$
$n = - 6$ $color(green)(n =-6)$

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

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

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

$5 m + n = 39$ $5m + n =39$

$5 \cdot (27 + 3 n) + n = 39$ $5 * (color(green)( 27 + 3n)) + n =39$

$5 \cdot (27) + 5 \cdot (3 n) + n = 39$ $5 * (color(green)( 27 )) + 5 * color(green)(( 3n)) + n =39$

$135 + 15 n + n = 39$ $135 + 15n+ n =39$

$135 + 16 n = 39$ $135 + 16n =39$

$16 n = - 96$ $16n =-96$

$n = - \frac{96}{16}$ $n =-96/ (16)$

$n = - 6$ $color(green)(n =-6)$

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

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

$m = 27 - 18$ $m = 27 - 18$

$m = 9$ $color(green)(m = 9$

How do you solve 5m+n=395m+n=39 and m−3n=27m-3n=27 using substitution?