How do you solve by substitution $m + n = 5$ and $m – n = 3$ ?

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Answer 1 · 2015-06-25T12:30:46

First solve one variable in terms of the other.

$m-n=3$ add $n$ on both sides:
$m=n+3$

Now substitute this for $m$ in the other equation:
$(n+3)+n=5->2n+3=5->n=1$

Then use this to find $m$ :
$m=n+3=1+3=4$

Or:
$m+n=5->m=5-n->$
$(5-n)-n=3->5-2n=3->-2n=-2->n=1->m=5-1=4$
Or:
$m+n=5->n=5-m->$
$m-(5-m)=3->m-5+m=3->2m=8->m=4->n=5-4=1$

How do you solve by substitution m + n = 5m + n = 5 and m – n = 3m – n = 3?