# How do solve the following linear system?:  y = 4x + 4, 3x - y = -6 ?

May 21, 2018

$x = 2$ and $y = 12$

#### Explanation:

In two linear equation system, make one variable the subject and substitute that variable in the second equation.

$y = 4 x + 4$ $\to$ equation 1
$3 x - y = - 6$ $\to$ equation 2

Substitute $y$ from equation 1 to equation 2:

$3 x - \left(4 x + 4\right) = - 6$

$3 x - 4 x - 4 = - 6$

$- x - 4 = - 6$

$- x = - 6 + 4$

$- x = - 2$

$x = 2$

Substitute $x = 2$ in equation 1 or equation 2 to get value of $y$.
Lets take equation 1:

$y = 4 x + 4$ $\to$ equation 1

$y = 4 \left(2\right) + 4$

$y = 8 + 4$

$y = 12$

So we get $x = 2$ and $y = 12$

$3 x - y = - 6$
$3 \left(2\right) - 12 = - 6$
$6 - 12 = - 6$
$- 6 = - 6$ $\to$ Correct