1. 3.5: Solving Nonlinear Systems

2. What is a nonlinear system?
We are used to solving systems where both lines were straight.
Nonlinear systems means at least one of the lines is not straight.
We will be working with quadratic functions (parabolas) for our nonlinear systems.

3. What could this look like?

4. What are solutions and how many could we have?

5. Solving by Graphing
Enter both equations into the graphing calculator for y1 and y2.
Graph the system.
Look for point(s) of intersection.
Estimate the points of intersection, check by substituting values into the equations OR
Utilize the table function to determine solutions.

6. EX 2:

7. Solution ex 2:

8. p. 136 #3 - 35

9. Solving by substitution:
Solve one of the equations for either x or y.
Substitute the expression into the second equation for the variable you solved for.
Solve for the variable. You may get to factor 
Plug the solution(s) into the first equation to determine the value(s) of the second variable.

10. Solution:

11. Substitution Ex 2: Solve the system by substitution: x2 + 2x – y = 5
Solutions (-6, 19) and (2, 3)

13. Solve systems by elimination:
Line up all like variables
Multiply (if needed) one or both equations to create a set of opposites. (+3x and -3x for example)
Add the equations together. One variable should eliminate out.
Solve for the remaining variable.
Substitute the solution(s) in and solve for the remaining variable.

14. Example 1:

15. Example 2:
2x2 + 4x – y = -2
x2 + y = 2
(-4/3, 2/9) and (0, 2)