1. How do you solve a system of quadratic and linear equations? x 2 +4x-8 =y 3x+5=y

2. In this lesson you will learn how to solve a system of a quadratic and linear equation by using substitution.

3. Let’s Review A system of equations: a group of two or more equations. A SOLUTION makes both equations true at the same time x 2 +4x-8 =y 3x+5=y

4. Let’s Review Substitution x 2 +4x-8 =y 3x+5=y x 2 +4x-8=3x+5 =y

5. A Common Mistake Solutions are coordinate pairs. They have an x AND a y value (4,6) (-1,-4)

6. Core Lesson Linear function x 2 -2x+1 =y y+3=x Quadratic function Use the quadratic function to substitute x 2 -2x+1 x 2 -3x+4 =0 y+3=x 7 3+i 2 (-3) 2 +4(1)(4) 3 2 7 3-i 2 x=

7. Core Lesson Remember, we need to find values for x and y. x 2 -2x+1 =y y+3=x We found x= y=x-3 7 3-i 2 or 7 3+i 2 y= -3 7 3-i 2 Y= 7 -3-i 2 y= -3 7 3+i 2 7 -3+i 2 Y=

8. Core Lesson Graphs have no intersection point -10 -5 5 15 20 25 30 -5510

9. In this lesson you have learned how to solve a system of a quadratic and linear equation by using substitution.

10. Guided Practice Solve the system of equations by substitution. y=x 2 +1 y-x=-1

11. Extension Activities Write a system of two equations, one linear and one quadratic, that have no real solutions.

12. If you needed to solve a quadratic equation which methods would you use, and why? Graphing? Taking a square root? Inspection? Factoring? Completing the square? Quadratic formula?

13. Quick Quiz What is the solution to this system of equations? How many times will a parabola and line cross if the system of equations has no real number solutions? y=x 2 -6x+5 y-2x=5