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

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Answer 1 · 2016-04-18T17:11:55

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

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

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

Substituting equation $2$ $2$ in $1$ $1$

$8 m + n = 34$ $8m + n = 34$

$8 \cdot (29 + 4 n) + n = 34$ $8 * (color(green)( 29 + 4n )) + n = 34$

$232 + 32 n + n = 34$ $232 + 32n + n = 34$

$33 n = 34 - 232$ $33n = 34 - 232$

$33 n = - 198$ $33n = - 198$

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

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

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

$8 m = 34 - n$ $8m = 34 - n$

$8 m = 34 - (- 6)$ $8m = 34 - (-6)$

$8 m = 34 + 6$ $8m = 34 + 6$

$8 m = 40$ $8m = 40$

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

$m = 5$ $color(blue)(m=5$

How do you solve 8m+n=348m + n = 34 and m−4n=29m - 4n = 29 using substitution?