1. Solving Nonlinear Systems of Equations
Keeper 9
GSE Accelerated Pre-Calculus

2. Solving a System of Equations
In the past, you studied two algebraic techniques for solving a system of linear equations. You can use the same techniques (substitution and linear combination) to solve quadratic systems.
Graphically
Elimination
Substitution

3. Tricks: Easy ways to Solve various systems of equations
Any conic with a line – Solve using substitution
Any conic with a circle – Solve graphically
Any conic with a hyperbola – Solve using elimination

4. Finding the Points of Intersection
Find the points of Intersection of the graphs of
𝑥 2 + 𝑦 2 =13
and
𝑦=𝑥+1.

5. Solving a System by Substitution
Find the points of intersection of the graphs in the system 𝑥 2 +4 𝑦 2 −4=0 −2 𝑦 2 +𝑥+2=0

6. Solving a System Using Elimination
Find the points of intersection of the graphs in the system. 𝑥 2 + 𝑦 2 −16𝑥+39=0 𝑥 2 − 𝑦 2 −9=0

7. Solving a System Graphically
Solve the following system by finding the intersection points. 𝑥 2 + 𝑦 2 =4 (𝑥+2) 2 + (𝑦−2) 2 =4

8. Turn it in… 𝑦=3𝑥−5; 𝑥 2 + 𝑦 2 =25 2𝑥+𝑦=15; (𝑥−2) 2 + 𝑦−1 2 =25
Solve by finding the intersection.
𝑦=3𝑥−5; 𝑥 2 + 𝑦 2 =25
2𝑥+𝑦=15; (𝑥−2) 2 + 𝑦−1 2 =25
𝑦=𝑥−4; (𝑥+2) 2 + 𝑦 2 =4
𝑥 2 + 𝑦 2 =4; (𝑥−3) 2 + (𝑦+3) 2 =9
(𝑥−1) 2 + 𝑦 2 =9; (𝑥−2) 2 + 𝑦 2 =4
(𝑥−4) 2 + 𝑦 2 =4; 𝑥 2 −8𝑥+ 𝑦 2 =−12