2.5.6 Lesson Summary

In this lesson, you learned how to:

• Explain why adding or subtracting two equations that share a solution results in a new equation that also shares the same solution.

Here are the activities that helped you reach those goals:

• 2.5.1: Writing and Evaluating New Equations
  • In this activity, you added equivalent values to both sides of an equation to evaluate if the equation was still true. By determining that the equation was still true, you discovered that adding equivalent values to each side of an equation maintains its truth.
• 2.5.2: Adding Two Equations in a System
  • In this activity, you wrote equations to represent constraints in a real-world situation. You then determined that adding these equations together results in a third equation with the same solution.
  • 2.5.2: Self Check
  • 2.5.2: Additional Resources
• 2.5.3: Solving Systems of Linear Equations in Two Variables
  • In this activity, you continued solving systems of equations in two variables by using an algebraic method of your own choice. You learned that some systems of equations are more suited to be solved by substitution and others by elimination.
  • 2.5.3: Self Check
  • 2.5.3: Additional Resources
• 2.5.4: Solving Systems of Equations Using Real-World Examples
  • In this activity, you analyzed a system of equations derived from a real-world situation. You reinforced that to solve a system using elimination by adding, the coefficients of one of the variables must be the same value and have opposite signs. If this is not the case, then no variable is eliminated when the resulting equation is created.

After these activities, you completed the following practice:

• 2.5.5: Practice