Algebra I - Unit 6: Topic 2 – Solving Systems by Elimination

Student Notes – Solving Systems by Elimination pp 397-403

To solve a system of equations by elimination:

a. First, line up the x’s, y’s, the equals, and the constants. b. Decide which variable is easiest to eliminate. c. Set up a “fair fight” to eliminate the variable. One should be equal, but opposite of the other.

You may need to multiply one equation by a negative number to set it up properly. d. Add your two equations to eliminate the variable. e. Keep substituting into the original equations until you get both x and y. f. Verify your solution.

Solve each system of equations by elimination. Write your answer as an _______________________.

1. 3 22 3x yx y� �

� �

3. 3 2 13 4 9x yx y� ��

Suppose you are asked to set up a “fair fight” between 2x and -4x: would they be equal but opposite? Explain Solve each system of equations by elimination.

5. 2 3 74 6 2x yx y� �

2. 2 54

x yx y�

� �

4. 3 52 10x yx y� �

6. 3 5 342 3 22x yx y� �

Algebra I - Unit 6: Topic 2 – Solving Systems by Elimination

7. David and Jose went to Target to buy clothes. David bought two shirts and one pair of jeans for $53.50. Jose bought two shirts and three pairs of jeans for $108.50. How much is one pair of jeans?

Algebra I - Unit 6: Topic 2 – Solving Systems by Elimination

Practice – Solving Systems by Elimination pp 397-403 Name _____________________________________ Date ___________________________ Period______________ Solve each system by elimination.

1. 2 3

2 5 9x y

x y�

� � �

2. 3 65 10x yx y� �� �

3.

15 30

21

7 62

x y

x y

�

�

4. 5 2 43 9x yx y� �

5. 3 5 13

2 5x y

x y� �

6. 4 3 93 4 12x yx y� �

Algebra I - Unit 6: Topic 2 – Solving Systems by Elimination

7. Three hundred fifty-eight tickets were sold to the school basketball game on Friday. Student tickets

were $1.50 and non-student tickets were $3.25. The school made $752.25. How many student and non-student tickets were sold?

8. Naomi took a 40-question history exam. The exam only had multiple-choice questions and short-answer questions. Each multiple-choice question was worth one point; each short-answer question was worth five points; the whole exam was worth 100 points.

A. Which system of equation could be used to solve for m, the number of multiple-choice questions, and s, the number of short-answer questions?

A 5 40

100m s

m s� �

C 40

5 100s ms m� �

B 40

5 100m sm s� �

D 5 40

100s m

s m� �

B. Solve the system that you selected in part A.

9. Karrie and Amy were shoulder partners. They both worked the same problem, but got two different answers. Who is incorrect and explain the error they made?