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

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

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

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

7. Solve the System Algebraically Use Substitution
(2, 2)
Answer: (2,2)

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)

10. 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 )

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

12. Equations must be solved for y!!
Zoom 6: ZStandard
The first equation can be entered as two separate entries:                    
or a "list" notation may be used:                         
Zoom 5: ZSquare
Answer: (5, –1) (1, – 5)