# How do you find the values of m and n that make the equation (m+2n)+(2m-n)i=5+5i true?

Nov 9, 2016

Please see the explanation for steps leading to the answer:

$m = 3 , n = 1$

#### Explanation:

Write two equations:

$m + 2 n = 5 \text{ [1]}$
$2 m - n = 5 \text{ [2]}$

You can use a matrix but it is just as easy to multiply the second equation by 2 and add to the first:

$5 m = 15$

$m = 3$

Substitute 3 for m in equation [1]:

$3 + 2 n = 5$

$n = 1$