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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