1. Section 3.5 Systems of Nonlinear Systems
Honors Algebra 2
Section 3.5
Systems of Nonlinear Systems

2. System of nonlinear equations- system of equations that contains at least one nonlinear equation

3. Finding points of intersection by graphing
Enter equations into 𝒚=
Choose a point to find
Press 2nd TRACE #5
Arrow spider to the left ENTER
Arrow spider to the right Enter Enter
The answer is at the bottom of the screen

4. Make sure you find all the intersection points.

5. Finding the right window
#1 Look at the equations so you know the parent functions you are dealing with. #2 Make sure your window is big enough to see all the places where the graphs intersect.

6. When your graphs don’t intersect, there is no solution to the system of equations.

7. Finding points of intersection by substitution
This method works well if one of the equations is linear.
Solve the following system using the substitution method.
𝑥 2 +2𝑥−𝑦=5
2𝑥+𝑦=7
Make sure you give answers as ordered pairs!!!!!

8. Finding points of intersection by elimination
This method (sometimes referred to as linear combinations) works well if you can eliminate the 𝑥 2 term.
Solve the following system using the elimination method.
3 𝑥 2 +2𝑥−2𝑦=10
𝑥 2 −6𝑥+2𝑦=−12

9. When using a calculator, irrational answers will be in estimated form.
To get exact irrational answers, you must use the substitution or elimination method.

10. New parent!!!!! This is not a function!!!!!
The standard form of a circle is
𝑥 2 + 𝑦 2 = 𝑟 2
The center is at 0,0 with radius r.
How can you differentiate a circle from a parabola?
𝑥 2 =5+𝑦 𝑥 2 + 𝑦 2 =36

11. Assignment #13
Pg. 136 #3-7 odd, all, odd, odd, 35, 36, 38, 50