Unit # 2 – Solving Systems of Linear and Quadratic Equations
Math 2
Unit 2.8 Solving Systems of Linear and Quadratic Equations
Types of Solutions Produced By a Linear and Quadratic System
Name: _______________
Example 1:
y x2 2x 3
y 2x 3
8
6
4
2
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -2 -4 -6 -8
Example 2:
y x 22 5
y 5
8
6
4
2
-6 -5 -4 -3 -2 -1 1 2 3 4 5 6 -2 -4 -6 -8
Example 3:
y x2 2x 4
y x 1
6 5 4 3 2 1
-4 -3 -2 -1 -1 -2 -3 -4 -5 -6
1234
Number of Solution(s): _______ Number of Solution(s): _______ Number of Solution(s): _______
What are the solutions?
What are the solutions?
What are the solutions?
Solving Linear and Quadratic System By Graphing Examples
Example 4a:
y x 22 6
y 4x 2
Example 5a:
y x2 2x 3
y 5
Example
6a:
y
x2
2x 7
y 2x 2
8
8
10
6
6
8
6
4
4
4
2
2
2
-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 -2 -4 -6 -8
-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 -2 -4 -6 -8
-10 -8 -6 -4 -2 -2 -4 -6 -8
-10
2 4 6 8 10
Solution(s): ______________ Solution(s): ______________ Solution(s): _______________
Solving Linear and Quadratic System By Substitution (Rework Examples Above) Examples
Example 4b:
y x 22 6
y 4x 2
Example 5b:
y x2 2x 3
y 5
Example
6b:
y
x2
2x 7
y 2x 2
Math 2 ? Linear and Quadratic Systems of Equations WS
Name: _________________________________
I. Solve each linear and quadratic system BY GRAPHING. State the solution(s) on the line. Must be ACCURATE!
1.)
y x2 2x 3
y 2x 1
2.)
y
x2
6x 6
y 3
3.)
y x 22 5
y x 1
y x2 4x 2
4.)
3
y 4 x 1
Solution(s): ______________ Solution(s): _______________ Solution(s): _______________ Solution(s): _______________
II. Solve each linear and quadratic system BY SUBSTITUTION. State the solution(s) on the line. Must SHOW WORK!
5.)
y
x2
5x
2
Solution(s):
_______
y 3x 2
6.)
y
x2
3x 2
Solution(s):
______
7.)
y
2x 2
4x
1
Solution(s):
_____
y x 6
y 2x 4
8.)
x
y
y 5 1 3x2
2x
Solution(s): _______
9.)
x2
y
8
0
Solution(s):
_______
x y 2 0
10.)
5x
y
2x2
6
Solution(s):
_____
y 4x 7x 2
................
................
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