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:

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

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

Then subtract 2x from both sides to get

When we factor, we get

Set each factor equal to 0

and

We find that

Now to get the y values, we substitute these x values into an equation. If we substitute them into then we have

which simplifies to

which simplifies to

Therefore, (0,-2) and (-2,-6) are the solutions to this system of equations.

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