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

Name Date

WORKSHEET 3.17: SOLVING SYSTEMS OF EQUATIONS USING

THE SUBSTITUTION METHOD

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Follow the steps below to solve a system of equations:

1. Solve one equation for one of the variables.


2. Substitute this expression in the other equation and solve.


3. Substitute this number in either one of the original equations and solve for the other
   variable.


4. Check your answer by substituting the values in both of the original equations.

EXAMPLE

Solve the system of equations: 2 x+ 4 y= 12

x+y= 5

Solve forx:x+y= 5 x= 5 −y.

Substitute 5 −yforxin the first equation and solve fory:2(5−y)+ 4 y= 12 →y= 1.

Substitute this value ofyin either equation. Ifyis substituted in the second equation,

x+ 1 = 5 →x= 4.

Check your answer.

2 x+ 4 y= 12 2(4)+4(1)= 12

x+ y= 54 + 1 = 5

DIRECTIONS: Solve each system of equations using the substitution method.

1. x= 2 y 2. a=− 2 +b 3. a=b+ 8
   x+y= 9 a+b=− 62 a=b


2. 2 x− 3 y= 5 5. 3 y−x= 4
   x+ 3 y=− 2 x= 7 + 2 y

CHALLENGE:William tried to solvex= 10 − 2 yandy−x=5. He substituted

10 − 2 yforxin the second equation. He goty− 10 − 2 y=5 and found

y=−15. By substitutingy=−15 in the first equation he foundx=40. But

the answer did not check. Find his error and the correct solution.

121

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