# How do you solve the system x=2y+7 and x=y+4 using substitution?

Mar 18, 2017

$y = - 3$ and $x = 1$

#### Explanation:

We know $x = y + 4$ Plug that into $x = 2 y + 7$ for x:

$y + 4 = 2 y + 7$

Move the $y$ to one side by subtracting y on both sides:

$y + 4 - y = 2 y + 7 - y$

$4 = y + 7$

Subtract 7 on both sides:

$4 - 7 = y + 7 - 7$

$- 3 = y$

Personally, I like the y on the other side. You are allowed to flip the equation around:

$y = - 3$

Now plug this in to one of the equations. I will plug it into the second equation:

$x = - 3 + 4$

$x = 1$

Check by plugging in to the other equation:

$1 = 2 \left(- 3\right) + 7$

$1 = - 6 + 7$

$1 = 1$

It works out!