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MA.912.A.3.14 Solving Systems of Linear Equations

What You Need To Know...

Solve systems of linear equations  in two variables.

  1. The benchmark will be assessed using MC (Multiple Choice) and FR (Fill in Response) items.
  2. Items may ask students to write a system of equations or to solve a system of equations.

Example One

Russ bought 3 medium and 2 large submarine sandwiches for a total of $29.95. Stacy bought 4 medium and 1 large submarine sandwiches for a total of $28.45.

Which statement shows the cost of each medium and each large sandwich?

A. Each medium sandwich costs $5.69 and each large sandwich costs $6.89.
B. Each medium sandwich costs $5.69 and each large sandwich costs $6.39. 
C. Each medium sandwich costs $5.39 and each large sandwich costs $6.89. 
D. Each medium sandwich costs $5.39 and each large sandwich costs $6.39. 

 

CLICK HERE FOR SOLUTION 

Example Two

A website that sells songs for downloading increased its price per song from $0.99 to $1.29. Macy spent $15.36 downloading songs during the month of the price increase. She downloaded 4 more songs at $0.99 than at $1.29.  The set of equations below represents the situation where x is the number of songs Macy downloaded at $0.99 and y is the number of songs she downloaded at $1.29.

x = y + 4
0.99x + 1.29y = 15.36

What is the exact number of songs Macy downloaded at the $0.99 price?

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CLICK HERE FOR SOLUTION

Additional Examples

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Solve by Graphing

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Solve by Substitution

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Solve by Elimination

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Application of Systems

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Reference Sheet