1. Solving Systems of Linear and Quadratic Equations

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

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

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

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

6. Try the following. (12,1) Many solutions Same Line! NO solution1.
Many solutions
Same Line! 4. 5. 2. 3.
NO solution
Parallel Lines! 6.
(12, – 4)

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

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

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

12. Solve the System Algebraically Use ????

13. 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 )

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