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

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WORKSHEET 3.18: SOLVING SYSTEMS OF EQUATIONS USING

THE ADDITION-OR-SUBTRACTION METHOD

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To solve systems of equations with the addition-or-subtraction method, do the following:

1. Decide if you will add or subtract to obtain an equation that has only one variable. If the
   coefficients of one of the variables are opposite, add the equations. If the coefficients
   of one of the variables are the same, subtract the second equation from the first. Solve
   the equation.


2. Substitute the value of the variable in one of the original equations and solve.


3. Check your solution in both of the original equations.

EXAMPLES

Addition method Subtraction method

3 x− 2 y= 13 3 x+ 5 y= 10

4 x+ 2 y= 8 Add to eliminate they-terms. 3 x+ y= 2 Subtract to eliminate thex-terms.

7 x=21 Solve forx.4y=8Solvefory.

x= 3 y= 2

3(3)− 2 y= 13 3 x+5(2)= 10

9 − 2 y= 13 3 x+ 10 = 10

− 2 y= 43 x= 0

y=− 2 x= 0

DIRECTIONS: Solve each system of equations.

1. 2 a− 3 b= 12 2. 4 a−b= 10 3. 5 x− 5 y= 0
   a+ 3 b= 6 − 4 a+ 8 b= 32 5 x− 2 y= 6


2. a−b= 2 5. 8 a+ 3 b=− 27
   − 3 a+b=− 22 a− 3 b=− 3

CHALLENGE:Canx− 8 y=−40 and− 5 x= 8 − 8 ybe solved using the

addition-or-subtraction method? Explain your reasoning and solve the

problem, if possible.

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