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

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Answer 1 · 2016-04-18T17:11:55

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

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

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

Substituting equation $2$ in $1$

$8m + n = 34$

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

$232 + 32n + n = 34$

$33n = 34 - 232$

$33n = - 198$

$n = - 198/33$

$color(blue)(n = - 6$

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

$8m = 34 - n$

$8m = 34 - (-6)$

$8m = 34 + 6$

$8m = 40$

$m = 40 / 8$

$color(blue)(m=5$

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