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Algebra 1

2.6.4 Building Equivalent Systems

Algebra 12.6.4 Building Equivalent Systems
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Here is a system of equations:

{12a+5b=−158a+b=11{12a+5b=−158a+b=11

To solve this system, Diego wrote these equivalent systems for his first two steps.

Step 1

{12a+5b=−15−40a+−5b=−55{12a+5b=−15−40a+−5b=−55

Step 2

{12a+5b=−15−28a=−70{12a+5b=−15−28a=−70

1.

Describe the move that Diego made between the original system and step 1.

2.

How do you know the system of equations in step 1 is equivalent to the original system?

3.

Describe the move that Diego made between step 1 and step 2.

4.

How do you know the system of equations in step 2 is equivalent to the ones in step 1 (and to the original system)

5.

Write another set of equivalent systems (different from Diego's first two steps) that will allow one variable to be eliminated and enable you to solve the original system. Be prepared to describe the moves you make to create each new system and to explain why each one has the same solution as the original system.

6.

Use your equivalent systems to solve the original system. Then, check your solution by substituting the pair of values into the original system.

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