The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 3.21: SOLVING SYSTEMS OF EQUATIONS THAT

HAVE ONE SOLUTION, NO SOLUTION, OR AN INFINITE NUMBER

OF SOLUTIONS

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To solve a system of equations, try to eliminate one of the variables and then follow the steps

below:

1. If only one of the variables is eliminated, the system of equations has only one solu-
   tion. You can find this solution by substituting the value for the variable in one of the
   equations and solving for the other variable.


2. If both variables are eliminated and the equation is true, there is an infinite number of
   solutions.


3. If both variables are eliminated and the equation is false, there is no solution.

EXAMPLES

Solve each system of equations.

y−x= 1 −x+ 2 y= 22 x+y= 4

y+x= 9 x− 2 y=− 2 − 2 x−y= 6

2 y= 10 0 = 00 = 10

y= 5 True statement False statement

Substitute 5 fory. Infinite number of solutions No solution

5 +x= 9

x= 4

DIRECTIONS: Solve each system of equations, or write ‘‘infinite number of solutions’’ or

‘‘no solution.’’

1. x= 2 y 2.x+ 2 y= 8 3. x−y= 6
   x− 2 y= 4 x−y=− 42 x+y= 3


2. 2 x+ 2 y= 10 5.− 3 x+ 4 y=− 6
   x+y= 55 x− 6 y= 8

CHALLENGE:By using guess and check, Jay found that the solution to the

system of equationsx+y=3and2(x+y)=6isx=1andy=2. Do you

agree? Explain your answer.

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.