Solving Systems of Linear and Quadratic Equations

Visualize all of the possible solutions to 2 lines 1 solution as an Ordered pair Infinitely man solutions—same line No solution– Parallel Lines

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)

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

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

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)

Solve the System Algebraically Use ????

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

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