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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.

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