Solving Quadratic Systems

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Presentation transcript:

Solving Quadratic Systems Topic 7.7

Ways to Solve Systems 1. Graphing 2. Algebraically Substitution Elimination can be used, but substitution is typically easier

Solving by Graphing Rewrite each equation for “y=” If you take the square root, remember that the answers are “±” the expression Graph the equations On the Casio, Press “F5” then “F5” again (isect) Make sure to choose the two equations that are intersecting If there is more than one intersection, move the direction key to get the others

Example: Solve the systems of equations graphically Answers: (0,2) and (4,6) Answers: (5,4) and (2,-4)

Solving Algebraically Use Substitution Solve the easiest equation for one variable Plug it into the second equation to get the value(s) of one variable Plug those value(s) back into the first equation to get the value(s) of the other variable

Example 1: Rewrite 2nd equation for y Substitute into 1st equation for y Solve for x Plug into 2nd equation

Example 2: Rewrite first equation for y2 Substitute y2 in the 2nd equation Substitute x back in the 1st equation <-SAME->