How do you solve $7 m + n = 41$ $7m+n=41$ and $m - 9 n = 45$ $m-9n=45$ using substitution?

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Answer 1 · 2016-05-16T20:22:45

$n = - \frac{137}{32}$ $n=-137/32$
$m = \frac{1449}{224}$ $m=1449/224$

$7 m + n = 41$ $7m+n=41$

$7 m = 41 - n (1)$ $color(green)(7m)=41-n" (1)"$

$m - 9 n = 45 let's extend both side of equation by 7$ $m-9n=45" let's extend both side of equation by 7"$

$7 \cdot m - 7 \cdot 9 n = 7 \cdot 45$ $color(red)(7)*m-color(red)(7)*9n=color(red)(7)*45$

$7 m - 63 n = 315$ $color(green)(7m)-63n=315$

$41 - n - 63 n = 315$ $41-n-63n=315$

$41 - 64 n = 315$ $41-64n=315$

$- 64 n = 315 - 41$ $-64n=315-41$

$- 64 n = 274$ $-64n=274$

$n = - \frac{274}{64} = - \frac{137}{32}$ $n=-274/64=-137/32$

$use (1)$ $"use (1)"$

$7 m = 41 + \frac{137}{32}$ $7m=41+137/32$

$7 m = \frac{1312 + 137}{32}$ $7m=(1312+137)/32$

$7 m = \frac{1449}{32}$ $7m=1449/32$

$m = \frac{1449}{32 \cdot 7}$ $m=(1449)/(32*7)$

$m = \frac{1449}{224}$ $m=1449/224$

How do you solve 7m+n=417m+n=41 and m−9n=45m-9n=45 using substitution?