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Solving Quadratic-Quadratic Systems of Equations |
You have just learned that two quadratics can intersect each other at 0, 1, 2, 3 or 4 points.
This means that a quadratic-quadratic system of equations can have 0, 1, 2, 3 or 4 solutions.
| Like linear-quadratic systems of equations, the solutions of a
quadratic-quadratic system of equations can be found graphically or algebraically.
| Let's look at an example.
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EXAMPLE 1: | ||||||
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Solve the following quadratic-quadratic system by graphing:
1. 2.
Sketching the graphs of both equations can give you a good estimate of where they intersect. The graphs are drawn for you below. |
| Notice that the circle and the hyperbola intersect at 4 places. If you zoom in, you can estimate the points of intersection as: | |
Like linear-quadratic systems of equations, the solutions of quadratic-quadratic systems can also be found algebraically.
Click to review the strategies for solving systems of equations algebraically.
| For our example of this page, a good strategy (but not the only strategy) for solving the system would be the elimination method:
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Check out these challenging questions that will help you practice solving quadratic-quadratic systems of equations. |