# How do you solve the following system?:  y= x-6 , x + 2y = 3

Nov 16, 2015

Use substitution to find: $x = 5$, $y = - 1$

#### Explanation:

The first equation gives us an expression for $y$ that we can substitute into the second equation:

$3 = x + 2 y$

$= x + 2 \left(x - 6\right)$

$= x + 2 x - 12$

$= 3 x - 12$

Add $12$ to both ends to get:

$3 x = 15$

Divide both sides by $3$ to get:

$x = 5$

Then from the first equation:

$y = x - 6 = 5 - 6 = - 1$