# Solving a System of Equations Using Substitution (Linear & Quadratic)

In this video, we are going to look at how to solve a system of equations (linear and quadratic) by using substitution. These are solved similarly to how we would normally solve any other system of equations.
For example:
$y=x^2+4x-2$
$y=2x-2$
To solve, we are going to take 2x-2, which equals y, and substitute it into the first equation where we see y. Now we have
$2x-2=x^2+4x-2$
Since it is a quadratic, we want to get one side equal to 0 so we can factor. First add 2 to both sides to get
$2x=x^2+4x$
Then subtract 2x from both sides to get
$0=x^2+2x$
When we factor, we get
$0=x(x+2)$
Set each factor equal to 0
$x=0$ and $x+2=0$
We find that
$x=0,-2$
Now to get the y values, we substitute these x values into an equation. If we substitute them into $y=2x-2$ then we have
$y=2(0)-2$ which simplifies to $y=-2$
$y=2(-2)-2$ which simplifies to $y=-6$
Therefore, (0,-2) and (-2,-6) are the solutions to this system of equations.