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

Jun 25, 2015

First solve one variable in terms of the other.

#### Explanation:

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

Now substitute this for $m$ in the other equation:
$\left(n + 3\right) + n = 5 \to 2 n + 3 = 5 \to n = 1$

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

Or:
$m + n = 5 \to m = 5 - n \to$
$\left(5 - n\right) - n = 3 \to 5 - 2 n = 3 \to - 2 n = - 2 \to n = 1 \to m = 5 - 1 = 4$
Or:
$m + n = 5 \to n = 5 - m \to$
$m - \left(5 - m\right) = 3 \to m - 5 + m = 3 \to 2 m = 8 \to m = 4 \to n = 5 - 4 = 1$