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

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WORKSHEET 3.19: SOLVING SYSTEMS OF EQUATIONS USING

MULTIPLICATION WITH THE ADDITION-OR-SUBTRACTION

METHOD

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Follow the steps below to solve systems of equations using multiplication with the

addition-or-subtraction method:

1. Multiply one or both of the equations by a nonzero number to obtain two equations with
   the same or opposite coefficients of a variable.


2. Follow the steps for using the addition-or-subtraction method:
   
   
   • Add or subtract the equations to eliminate a variable.
   
   
   • Solve the new equation.
   
   
   • Substitute the value of the variable in one of the original equations and solve.
   
   
   
   


3. Check the solution by substituting both values in each of the original equations.

EXAMPLES

Solve 3 x− 5 y= 8 and− 2 x+ 3 y= 3. (To eliminate thex-terms, multiply the first equation by 2

and the second equation by 3.)

3 x− 5 y= 8 → 6 x− 10 y= 16

− 2 x+ 3 y= 3 →− 6 x+ 9 y=9Add

−y= 25

y=−25 Substitute−25 foryin one of the original equations

and solve. 3x−5(−25)=8;x=−39.

DIRECTIONS: Solve each system of equation by using multiplication with the

addition-or-subtraction method.

1. 3 x+ 2 y= 21 2. 9 y+ 7 x= 2 3. − 2 x+ 4 y=− 8
   7 x− 11 y= 22 y− 4 x= 63 x− 6 y= 12


2. − 6 x+ 3 y=− 6 5. 4 y+ 4 x= 12
   2 x+ 6 y= 30 2 y+x= 1

CHALLENGE:Consider the solution of 2x+ 3 y=11 and 4x− 5 y=−11. Is it

more efficient (less work) to eliminate they-terms first? Or is it more

efficient to eliminate thex-terms first? Explain your reasoning and solve

the system of equations.

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Copyright

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