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Solving Systems of Linear and Quadratic Equations

Solving Systems of Linear and Quadratic Equations

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Solving Systems of Linear and Quadratic Equations

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  1. Solving Systems of Linear and Quadratic Equations

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

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

  5. Try the following. (12,1) Many solutions Same Line! 1. 4. 5. 2. 3. NO solution Parallel Lines! 6. (12, – 4)

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

  7. Solve the System AlgebraicallyUse Substitution (0, 1) (1, 2) Answer: (0,1) (1,2)

  8. Solve the System AlgebraicallyUse Substitution (2, 2) Answer: (2,2)

  9. Solve the System AlgebraicallyUse Substitution (5, –1) (1, – 5) Answer: (5, –1) (1, – 5)

  10. Solve the System AlgebraicallyUse Substitution (4, 3) (– 4, – 3) Answer: (4, 3) (–4, – 3)

  11. Solve the System AlgebraicallyUse ????

  12. Now let’s look at the Graphs of these Systems! Quadratic What does the graph of each look like? Parabola 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 )

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