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

Name Date

WORKSHEET 3.20: SOLVING SYSTEMS OF EQUATIONS USING

A VARIETY OF METHODS

-------------------------------------------------------------------------------------

There are three methods for solving a system of equations:

1. Substitution— Use this method when the coefficient of one of the variables is 1 or−1.


2. Addition or subtraction— Use this method when the coefficients of one of the variables
   are the same or are opposites.


3. Multiplication with addition or subtraction— Use this method when the substitution and
   addition-or-subtraction methods cannot be used.

DIRECTIONS: Select the best method and solve each system of equations.

1. x+y= 3 2. x− 2 y= 0 3. x+ 2 y= 5
   − 2 y+x= 1 x+ 2 y= 12 − 2 x+ 3 y=− 3


2. 4 x+ 3 y= 16 5. 5 x− 2 y= 8 6. 3 x− 8 y= 7
   2 x− 3 y= 83 x− 5 y= 1 x+ 2 y=− 7


3. 2 x+ 3 y= 12 8. x+ 2 y= 5 9. 2 x+ 3 y= 4
   3 x+ 2 y= 13 − 2 x+ 3 y=− 35 x− 3 y= 10


4. x=− 15 y 11. 2 x+ 3 y= 16 12. 5 x= 10 y
   x+ 4 y= 33 3 x+ 4 y=− 12 − 4 x+ 10 y= 8

CHALLENGE:Describe a system of equations that can be solved most

efficiently by either the substitution method or the addition-or-subtraction

method.

127

Copyright

©

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