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Name: _____________________________________________________________
Date: _________________________
Period: ______
6-2
Chapter 6: Graphing
Topic 2: Solving Systems Algebraically
Recall: A system of equations means we are working with ________ equations
The solution set is all of the points (x,y) where the two graphs ___________________________.
Type 1: Quadratic-Linear System of Equations
The best method of solving is: ____________________________________
Example #1: Solve the system of equations
𝑦−𝑥 =1
𝑦 = −𝑥 2 + 6𝑥 − 3
Steps:
Work:
1.
2.
3.
4.
5.
Check in the calculator: Put each original equation into 𝑦 = form. Look at the graphs & where they intersect.
Name: _____________________________________________________________
Date: _________________________
Type 2: Quadratic-Quadratic System of Equations
The best method of solving is: ____________________________________
Example #2: Solve the system of equations
𝑥 2 + 4𝑦 2 = 25
𝑦 2 + 𝑥 2 = 13
Steps:
Work:
1.
2.
3.
4.
You try! Solve each of the following systems of equations in your notebook.
1. 𝑦 = 2𝑥 2 − 4𝑥 − 5
3𝑥 − 𝑦 = 1
2. y = x 2 − 4
𝑦 = −2𝑥 − 4
3. 𝑦 2 + 𝑥 2 = 25
𝑦 2 + 9𝑥 2 = 25
4. 𝑦 2 = 𝑥 2 − 7
𝑥 2 + 𝑦 2 = 25
Period: ______
6-2