## Solving Systems of Equations Algebraically

### Johnny WolfeSanta Rosa District Schools

#### Description

Student will solve a system of equations algebraically.

#### Objectives

Understands the relative size of integers, rational numbers, irrational numbers, real numbers and complex numbers.

Understands that numbers can be represented in a variety of equivalent forms using integers, fractions, decimals, and percents, scientific notation, exponents, radicals, absolute value, or logarithms.

Understands and explains the effects of addition, subtraction, multiplication and division on real numbers, including square roots, exponents, and appropriate inverse relationships.

Uses systems of equations and inequalities to solve real world problems graphically, algebraically, and with matrices.

#### Materials

- Overhead transparencies (if examples are to be worked on overhead) for Solving Systems of Equations Algebraically (see attached file).

- Solving Systems of Equations Algebraically Examples (see attached file).

- Solving Systems of Equations Algebraically Worksheet (see attached file).

- Solving Systems of Equations Algebraically Checklist (see attached file).

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for Solving Systems of Equations Algebraically Examples (see attached file).

2. Have marking pens (for overhead).

3. Have Solving Systems of Equations Algebraically Examples (see attached file) prepared and ready to demonstrate to students.

4. Have enough copies of Solving Systems of Equations Algebraically Worksheet (see attached file) for each student.

5. Have enough copies of Solving Systems of Equations Algebraically Checklist (see attached file) for each student.

#### Procedures

Prior Knowledge: Students should be familiar with basic operation skills such as addition, subtraction, multiplication, division, exponents, fractions, decimals, solving equations, and point-slope form of a linear equation. Note: This lesson does not address the following: irrational, and complex numbers; percents, scientific notation, exponents, radicals, absolute value, logarithms; square roots, exponents, and appropriate inverse relationships; inequalities, graphing, matrices. This lesson contains a checklist to assist the teacher in determining which students need remediation. The sole purpose of this checklist is to aide the teacher in identifying students that need remediation.

1. Explain the difficulty in solving a system of equations graphically (see # 1 on attached file Solving Systems of Equations Algebraically Examples). Answer student questions and comments.

2. Mention to students that there are other alternatives to solving a system of equations (see # 2 on attached file Solving Systems of Equations Algebraically Examples). Answer student questions and comments.

3. Demonstrate the substitution method for solving a system of equations (see # 3 on attached file Solving Systems of Equations Algebraically Examples). Answer student questions and comments.

4. Have the students solve a system of equations by substitution. Assist students in setting up the equations correctly (see # 4 on attached file Solving Systems of Equations Algebraically Examples). Answer student questions and comments.

5. Demonstrate the elimination method for solving a system of equations (see # 5 on attached file Solving Systems of Equations Algebraically Examples). Answer student questions and comments.

6. Discuss with students when to use substitution and elimination methods (see # 6 on attached file Solving Systems of Equations Algebraically Examples). Answer student questions and comments.

7. Demonstrate to students how to rewrite equations using multiplication and division techniques (see # 7 on attached file Solving Systems of Equations Algebraically Examples). Answer student questions and comments.

8. Have students solve a system of equations using elimination. Assist students in setting up correct equations (see # 8 on attached file Solving Systems of Equations Algebraically Examples). Answer student questions and comments.

9. Work example 9 (see attached file Solving Systems of Equations Algebraically Examples). Answer student questions and comments.

10. Work example 10 (see attached file Solving Systems of Equations Algebraically Examples). Answer student questions and comments.

11. Work example 11 (see attached file Solving Systems of Equations Algebraically Examples). Answer student questions and comments.

12. Distribute the Solving Systems of Equations Algebraically Worksheet (see attached file).

13. Distribute the Solving Systems of Equations Algebraically Checklist (see attached file). Describe what constitutes an “A,” “B,” “C,” “D,” and an “F” in the CHECKLIST.

14. The student will write their response on the worksheet.

15. The teacher will move from student to student observing the students work and lending assistance.

#### Assessments

Student worksheets will be taken up and scored according to “Solving Systems of Equations Algebraically Checklist”. These scores may be placed in the grade book.

#### Extensions

Place a system of equations on the board. Have 3 students solve the system, each working it using a different method (graphing, elimination, and substitution). Then have students look at the results and determine which method is best for that type of system.