1. Solving Systems of Linear and Quadratic Equations

2. Objectives I can solve systems of linear and quadratic equations by graphing them. I can solve systems of linear and quadratic equations algebraically.

3. System of Equations When you have 2 or more equations to solve at one time, we call this a system of equations. The solution set to the system is where the graphs intersect. The solution is an Ordered Pair (x, y)

4. MOST Important Step

5. Where the graphs CROSS? Remember that where are graphs cross are the solutions. The calculator finds the Intersection.

6. Lines intersect at one point: consistent & independent 2 Solutions 1 Solution No Solutions

7. Given the following system of equations, solve by graphing.

8. 1263457891010 4 3 2 7 5 6 8 9 x- axis y- axis 0 1-2-6 -3-4-5 -7-8-9 1010 -4 -3 -2 -7 -5 -6 -8 -9 0 (-.33,1.78) y = x 2 – 2x + 1 y=2/3x + 2 (3,4)

9. BIG PICTURE The solution to a system of equations is where the graphs cross! The solutions are always Ordered Pair Format! There are 3 types of solutions –One Solution (Ordered Pair) –Two Solutions (Ordered Pairs) –No Solutions

10. Algebraic Method 1. Get each equation isolated for “y” by itself 2. Substitute the LINEAR expression for “y” into the QUADRATIC equation for “y” 3. Solve that new Quadratic Equation –Set it equal to zero –Usually it will factor –Get the “x” solutions from each factor 4. Substitute each “x” value into the linear equation to find the “y” values.

11. Example for Notes

12. Homework WS 6-3 Quiz Next Class