We used the review of systems of linear equations on Friday to jump to systems of non-linear equations today. Our lesson has systems that are either 1 linear & 1 quadratic equation OR 2 quadratic equations.
Students should be able to find solutions on a graph. To do this, identify where the graphs meet. There could be no solutions (no intersection), 1 solution, 2 solutions, or infinitely many solutions (when the graphs overlap completely).
Students should also be able to find solutions by working with the equations. To do this follow these steps:
- Confirm that both equations are solved for y. If not, get y by itself.
- Substitute the first expression for y in the second equation. Solve for x. This can be done by either (1) setting the equation equal to 0, factoring, and solving for x from the factors; or (2), only when b = 0, set x2 equal to the constant value and then square rooting both sides. Remember, when using method #2, the solution is the positive & negative of the value acquired through square-rooting.
- Substitute the solved value(s) for x into either of the two equations and solve for y.
- To check the solutions, substitute the ordered pairs into both equations to verify the values are correct.
Example:
Homework: Worksheet on Solving Systems of Non-Linear Equations.
There will be a TEST on Thursday covering all quadratic concepts from last week and this week. Students will receive a review worksheet tomorrow in class.
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