1. Lesson 9.7 Solve Systems with Quadratic Equations
Essential Question: How do you solve systems that include a quadratic equation?
Warm-up:
CC.9.12.A.REI.4b
Solve quadratic
equations by
inspection, by
taking square roots,
completing the
square, the quadratic
formula and factoring,
as appropriate to the
initial form of the
equation. Recognize
when the quadratic
formula gives complex
solutions.
1. Solve the linear system using substitution.
y = 3 – 2x
y = x + 9
Solve the linear system using elimination.
x – y = 10
4x + y = -15

2. Remember these? Systems of Linear Equations
We had 3 methods to solve them.
Method 1 - Graphing
Solve for y.
(6, – 4)

3. Remember these? (6, – 4) Systems of Linear Equations
Method 2 - Substitution
(6, – 4)

4. Remember these? (6, – 4) Systems of Linear Equations
Method 3 - Elimination
All 3 methods giving us the same answer (6,–4).
(6, – 4)

5. Solving Systems of Linear and Quadratic Equations

6. Now let’s look at
Systems of
Linear and Quadratic
Equations!

7. Substitution Method
Step 1: Solve one of the equations for one of its variables.
Step 2: Substitute the expression from step 1 into the other equation and solve for the other variable.
Step 3: Substitute the value from step 2 into one of the original equations and solve.

8. Example 1 Use Substitution Method
Solve the system:

9. Systems with One Linear Equation and One Quadratic Equation
No solution
One Solution
Two Solutions

10. Solve the System Algebraically Use Substitution
(0, 1)
(1, 2)
Answer: (0,1) (1,2)

11. Solve the System Algebraically Use Substitution
(2, 2)
Answer: (2,2)

12. Solve the System Algebraically Use Substitution
(5, –1)
(1, – 5)
Answer: (5, –1) (1, – 5)

13. Solve the System Algebraically Use Substitution
(4, 3)
(– 4, – 3)
Answer: (4, 3) (–4, – 3)

14. Now let’s look at the Graphs of these Systems!
Quadratic
Parabola
What does the graph of each look like?
Classify each equation as linear/quadratic.
Linear
Line
What is the solution to the system?
Point of Intersection
(-2, 0)
Point of Intersection
(1, -3 )

15. We have solved the following algebraically
Now use your calculator to check it graphically.
Answer:
(0,1) (1,2)
Answer:
(2,2)

16. Quiz on Quadratic formula on Tuesday!
Classwork/Homework
9.7 Exercises
Pages 625
2- 20 even
Quiz on Quadratic formula on Tuesday!