# How do you solve xy=144 and x-y=18?

Apr 22, 2016

Use substitution and factoring

#### Explanation:

$x y = 144$
$x - y = 18$
$\therefore x = 18 + y$

Substituting this into the first equation gives
$\left(18 + y\right) y = 144$
$18 y + {y}^{2} - 144 = 0$
$\left({y}^{2} + 18 y - 144\right) = 0$
$\left(y + 24\right) \left(y - 6\right) = 0$

$y = - 24$ or $y = 6$
$x = - 6$ or $x = 24$