# How do you solve the system y = -3x + 6 and 3x-y = 6?

Jan 14, 2016

$x = 2$
$y = 0$

#### Explanation:

The equations are

1. $y = - 3 x + 6$
2. $3 x - y = 6$

Solve the value of $x$ by substitution

$3 x - y = 6$
$3 x - \left(- 3 x + 6\right) = 6$, plug in the value of y
$3 x + 3 x - 6 = 6$, simplify and combine like terms
$6 x = 12$, isolate x
$\frac{\cancel{6} x}{\cancel{6}} = \frac{12}{6}$
$x = 2$

To find the value of $y$, where

$y = - 3 x + 6$, plug in the value of x
$y = - 3 \left(2\right) + 6$, simplify
$y = - 6 + 6$
$y = 0$

Checking:

1. $y = - 3 x + 6$
$0 = - 3 \left(2\right) + 6$
$0 = - 6 + 6$
$0 = 0$

2. $3 x - y = 6$
$3 \left(2\right) - 0 = 6$
$6 - 0 = 6$
$6 = 6$