2.6.6 Lesson Summary

In this lesson, you learned how to:

• Explain how multiplying equations by a factor can help us solve systems of linear equations.

Here are the activities that helped you reach those goals:

• 2.6.1: Multiplying Equations by a Number
  • In this activity, you use technology to graph a system of equations. Then you created new equations by multiplying any of the original equations by the same number. After graphing these new equations, you learned that multiplying an entire equation by a number does not change its solution.
• 2.6.2: Writing a New System to Solve a Given System
  • In this activity, you reviewed the process of multiplying one equation in a system of equations by a single number to form a new system of equations in order to solve by elimination. By solving the new system of equations, you showed that the solution to the system of equations was not changed from the original system of equations.
  • 2.6.2: Self Check
  • 2.6.2: Additional Resources
• 2.6.3: Finding Solutions to Unordered Sets of Equivalent Systems
  • In this activity, you used your knowledge of solving systems of equations to correctly order the steps used when solving a system by elimination when multiplication is needed in both original equations.
  • 2.6.3: Self Check
  • 2.6.3: Additional Resources
• 2.6.4: Building Equivalent Systems
  • In this activity, you showed that there are multiple ways to solve a system of equations using elimination. Since any one of the original equations can be multiplied by any number without changing the validity of the equation, there are many ways to cancel out a variable when combining the equations in the system.

After these activities, you completed the following practice:

• 2.6.5: Practice