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**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

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**Remember these? Systems of Linear Equations**

We had 3 methods to solve them. Method 1 - Graphing Solve for y. (6, – 4)

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**Remember these? (6, – 4) Systems of Linear Equations**

Method 2 - Substitution (6, – 4)

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**Remember these? (6, – 4) Systems of Linear Equations**

Method 3 - Elimination All 3 methods giving us the same answer (6,–4). (6, – 4)

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**Solving Systems of Linear and Quadratic Equations**

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

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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.

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**Example 1 Use Substitution Method**

Solve the system:

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**Systems with One Linear Equation and One Quadratic Equation**

No solution One Solution Two Solutions

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**Solve the System Algebraically Use Substitution**

(0, 1) (1, 2) Answer: (0,1) (1,2)

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**Solve the System Algebraically Use Substitution**

(2, 2) Answer: (2,2)

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**Solve the System Algebraically Use Substitution**

(5, –1) (1, – 5) Answer: (5, –1) (1, – 5)

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**Solve the System Algebraically Use Substitution**

(4, 3) (– 4, – 3) Answer: (4, 3) (–4, – 3)

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**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 )

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**We have solved the following algebraically**

Now use your calculator to check it graphically. Answer: (0,1) (1,2) Answer: (2,2)

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**Quiz on Quadratic formula on Tuesday!**

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

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