# How do you solve y² = x + 3 and x - 2y = 12 using substitution?

May 4, 2016

See solution below.

#### Explanation:

$x = 12 + 2 y \to {y}^{2} = 12 + 2 y + 3$

${y}^{2} - 2 y - 15 = 0$

$\left(y - 5\right) \left(y + 3\right) = 0$

$y = 5 \mathmr{and} - 3$

$x - 2 \left(5\right) = 12 \mathmr{and} X - 2 \left(- 3\right) = 12$

$x = 22 \mathmr{and} x = 6$

Your solution set is $\left\{22 , 5\right\} \mathmr{and} \left\{6 , - 3\right\}$

Hopefully this helps!