Vista Grande High School

Systems of Equations Unit

Algebra 2

W, 2/9 / F, 2/11
Solving y Graphing 7.1
Page 401: 11-25,
47 - 58 / Solving by Substitution 7.2
Pg. 408: 17–22, 54-63
M, 2/14 / W, 2/16 / F, 2/18
Solving by Combining 7.3
Pg. 414: 8-13, 16-18, 31-33, 57-59, 63-66 / Solving Using all 3 Methods 7.4
Pg. 421: 13-15, 19 – 27, 31-33 / Writing Word Problems to Model Systems
Modeling Linear Systems Worksheet
M, 2/21 / W, 2/23 / F, 2/25
Special Types of Linear Systems 7.5
Pg. 430: 12-23 / Solving Linear Inequalities by Graphing 7.6
Pg. 435: 9 – 20 / Review Systems
W, 2/28
Test on Systems

Materials available at spartansmath.wikispaces.com or spartansmathdolezal.wikispaces.com

Math Help Available: Black Lunch – Room 1218 (Ms. Wildermuth) or Gold Lunch – Room 1215 (Mrs. Hodge)

On-line book available by going to

http://www.classzone.com/books/algebra_1/ and creating an account.

Book ISBN: 0618250182
ALGEBRA 2 – UNIT 1

LESSON 1: SOLVING SYSTEMS OF EQUATIONS BY GRAPHING

Graphing Review

Graph each equation.

1. 2.

3. 5.

5. 6.

IDENTIFYING SOLUTIONS OF EQUATIONS

Review: A solution of a linear equations is a ______.

System of equations:

Solution:

· An ordered pair that makes ______.

· Also, the ______of the lines.

Determine whether the point is a solution of the system.

1. 2.

3. 4.

Solve each system of equations by graphing.

1. 2.

3. 4.

LESSON 2 – SOLVING SYSTEMS OF EQUATIONS BY SUBSTITUTION

WARM UP

1. Determine whether (-1, 7) is a solution to the system:

Solve each system by graphing.

2. 3.

Lesson 2: Solve each system of equations by substitution.

1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

11. 12.

LESSON 3 – SOLVING SYSTEMS OF EQUATIONS BY ELIMINATION (ADDITION)

WARM UP

Solve each system of equations by the substitution method.

1. 2.

Lesson 3: SOLVING SYSTEMS BY ELIMINATION

Start by combining these like terms:

a. b. c.

d. e. f.

Question: The ones that add up to equal 0, what kind of numbers are being added together?

With two equations, we can add them together, and the opposites will cancel out. This gives us an equation with only one variable…and we know how to do that.

Solve each system using elimination (addition).

1. 2.

3. 4. 5.

Sometimes the variables won’t cancel out right away. So, you have to use a multiplier to make one of the variables cancel out (eliminate).

6. 7.

8. 9.

10. 11.

LESSON 4 – SOLVING (NUMBER) WORD PROBLEMS

WARM UP

Solve the system using 3 different methods: graphing, substitution and elimination.

Graphing Substitution Elimination

a. b. c.

Lesson 4 : Writing Systems of equations to find two numbers.

1. The sum of two numbers is 16. Their difference is 8. Find the two numbers.

2. The sum of two numbers is 35. Their difference is 7. Find the two numbers.

3. The sum of two numbers is 101. Their difference is 1. Find the two numbers.

4. The sum of two numbers is 25. When 4 times the smaller number is subtracted from three times the larger number, the result is 5. What is the larger of the two numbers?

5. The sum of two numbers is 18. When five times the smaller number is subtracted from six time the larger number, the result is 31. What is the larger of the two numbers?

6. The difference between two numbers is 9. Three times the smaller number plus five times the larger number is 61. What are the two number?

7. Four burritos and three tacos cost $39. Three burritos and five tacos cost $43. What is the cost of a burrito? A taco?

8. Four pepperoni pizzas and five cheese pizzas cost $67. Three pepperoni pizzas and two cheese pizzas cost $38. What is the cost of a pepperoni pizza? A cheese pizza?

LESSON 5: SPECIAL TYPES OF LINEAR SYSTEMS

Warm Up

Use the addition method (elimination) to solve each system.

1. 2x + 4y = -1 2. 3x – 4y = -20

6x + 4y = 3 x + 2y = -10

Find the two numbers for each word problem.

3. The sum of two numbers is 20. The difference of the two numbers is 2. Find the two numbers.

4. The sum of two numbers is 30. Six times the smaller number minus the larger numbers gives a result of 40. What are the two numbers?

LESSON 5: SPECIAL TYPES OF LINEAR SYSTEMS.

There are three different possible solutions when solving a linear system:

Line Intersect Lines are Parallel Lines Coinside

One solution No solution Infinitely many solutions

Example 1: A Linear System with No Solution.

Show that the linear system has no solution:

Example 2: A Linear System with Many Solutions.

Show that the linear system has infinitely many solutions:

Example 3: Identifying the Number of Solutions

Solve each system and interpret the results.

a. b. c.

d. e. f.