# How do solve the following linear system?:  5x+2y=4 , y=-3x+4 ?

Mar 11, 2018

$x = 4 , y = - 8$

#### Explanation:

$5 x + 2 y = 4$
$y = - 3 x + 4$

Since the second function already has the y term isolated, plug it in for y in the first function to solve for x

$5 x + 2 \left(- 3 x + 4\right) = 4$ (Distribute the 2)

$5 x - 6 x + 8 = 4$ (Combine like terms)

$- x + 8 = 4$ (Subtract 8 from both sides)

$- x = - 4$ (Divide both sides by -1)

$x = 4$

Now that you found the x variable, plug it into either equation to find y

$y = - 3 \left(4\right) + 4$ (Distribute -3)

$y = - 12 + 4$ (Find the difference/sum)

$y = - 8$

Check your answer by plugging it back into either of the original equations

$5 \left(4\right) + 2 \left(- 8\right) = 4$

$20 + \left(- 16\right) = 4$

$4 = 4$

This is how you solve by substitution