# Lesson 9.7 Solve Systems with Quadratic Equations

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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

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

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

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

Solving Systems of Linear and Quadratic Equations

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

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.

Example 1 Use Substitution Method
Solve the system:

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

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

Solve the System Algebraically Use Substitution

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

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

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 )

We have solved the following algebraically