Pre-AP Algebra 2 Lesson 2-2 Determining the number of ... - Denton ISD

[Pages:4]Pre-AP Algebra 2 Lesson 2-2 ? Determining the number of solutions to a 2x2 system; Intro to 3x3 systems

Objectives: The students will be able to: solve a 2x2 system of equations by elimination (review). determine the number of solutions that a 2x2 system has, both algebraically and graphically. solve a 3x3 system by elimination.

Materials: Hw #2-1 answers overhead; tally sheets; Do Now handout and answers overhead; note-taking templates; pair work; homework #2-2

Time 5 min 10 min 20 min

25 min

Activity Review Homework Show the answers to #2-1 on the overhead. Students correct their answers. Pass around a tally sheet. Homework Presentations Review the top 2 or 3 problems. Do Now Pass out the How Many Solutions Are There? worksheet. Students solve and graph three 2x2 systems of equations ? one has 1 solution, one has no solutions, and one has infinitely many solutions. While reviewing the answers on the overhead, help students make the connection between the number of solutions and the number of intersection points. Direct Instruction

Background Information:

A 2x2 System of Equations is a system of two equations with two variables that are solved together.

There are three possible outcomes with a 2x2 system:

Graph

Number of Solutions Equation (c = any #)

Lines intersect at 1 point 1

x = c

Lines are parallel

None

0 = c (never true!)

Lines are the same

Infinitely many

0 = 0 (always true!)

A 3x3 System of Equations is a system of three equations with three variables that are solved together.

Concepts: To solve a 3x3 system with linear combination:

1) Decide which variable is easiest to eliminate. 2) Eliminate that variable from one pair of equations. 3) Eliminate the same variable from a different pair of equations. 4) Write the resulting equations as a 2x2 system and solve it.

Notes:1) If the 2x2 has 0 or infinitely many solutions, the same is true about the 3x3 and you can stop there. 2) See if you can use division to simplify the new equations. 5) Plug in the solutions to one of the original equations and solve for the third variable. 6) Check by plugging in the solution to the other two original equations.

Example: Show students how to solve the system, alternating between the concept steps and the example steps.

3x y 2z 8

(0, 2, 5) is the solution.

2x y 4z 18

5x 2 y z 1

20 min

Pair Work Hand out the Solving 3x3 Systems Practice sheet for students to work on.

Pre-AP Algebra 2 Lesson 2-2 ? Bellringer

How Many Solutions Are There?

Directions: 1) Solve each system of equations algebraically. Two of them may seem to come out a little strange. Note: in each system, try to simplify the first equation by using division before you do anything else. 2) Graph each system of equations on the coordinate planes below. 3) Compare your algebraic and graphical solutions. What conclusions can you make about the relationship between the algebraic solution and the graph?

2x 4y 8 A)

3x y 3

6x 3y 3 B)

2x y 2

2x 4y 8 C)

x 2y 4

Conclusions:

Pre-AP Algebra 2 Lesson 2-2 ? Pairwork

Solving 3 x 3 Systems of Equations

1) Solve the 2 x 2 system. Use division to simplify the equations before you begin.

4x 8y 20 77x 77 y 77

2) Multiple Choice. Which ordered triple represents the solution to the system of equations?

2x y 3z 11 x 2y 4z 3

a. (-1, 1, -4) b. (1, 3, -2) c. (3, 8, 1) d. (2, -3, 0)

x 5y 2z 18

3) Solve each system of equations. Label each equation and organize your work neatly.

2x 3y z 5 3x 2 y z 5

3x 4 y 2z 8

x 2y z 2 2x 4y 2z 6

4x 5y 7z 3

Pre-AP Algebra 2 Lesson 2-2 ? Homework

3 x 3 Systems of Equations

Do all work on binder paper (stapled to the back). Write all answers on this page. Part 1: Multiple Choice. What is the solution to the system of equations?

2x y z 4

1) 4x 2 y 2z 8

x 3y z 5

a. (5, 4, -2) b. (0, -5, -1)

c. No Solution d. Infinitely Many Solutions

4x y z 3

2) 2x 3y 4z 5

10x y 5z 11

a. (-2, 3, -2) b. (-1, 1, 0)

c. No Solution d. Infinitely Many Solutions

Part 2: Free Response. Solve each system of equations. 3)

2x y 3z 8 x 6y z 0

6x 3y 9z 24

4)

x 3y z 12 x 4 y 2z 22 3x y z 16

5)

x 2 y z 12 x 2 y 3z 0

2x y 4z 24

Mega Bonus: +10 homework points!

To solve a 4x4 system, use elimination to reduce it to a 3x3 system, and then proceed from there. If you want to get this problem right, you need to stay super organized ? but everyone can do it if they try. You must show all work to get credit.

w 2x y 2z 10

w 3x 2 y z 0

2w x y 4z 13

3w x 5y z 7

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download