2.4.6 Lesson Summary

In this lesson, you learned how to:

• Solve systems of equations by adding or subtracting them to eliminate a variable.
• Demonstrate that adding or subtracting equations in a system creates a new equation, where one of the solutions to this equation is the solution to the system.

Here are the activities that helped you reach those goals:

• 2.4.1: Combining Two True Equations
  • In this activity, you analyzed a model representing the process of combining two different equations. You learned that when two equations that are true are combined, the resulting equation is also true.
• 2.4.2: Adding Equations
  • In this activity, you learned how to add two equations together into a third equation. By using elimination, you created a third equation containing only one variable. This third equation can be solved to find the value of one of the variables. Using this value, you can find the value of the remaining unknown variable. You used solutions to the first two equations to test that they were still true for the third equation.
  • 2.4.2: Self Check
  • 2.4.2: Additional Resourcess
• 2.4.3: Adding and Subtracting Systems of Equations and Using Their Graphs
  • In this activity, you added two equations to form a third equation. You then graphed the original system of equations alongside the new third equation. By determining that all three equations intersect at the same point, you verified that the solution to the first two equations is the same as the solution to the third equation.
  • 2.4.3: Self Check
  • 2.4.3: Additional Resourcess
• 2.4.4: Determining the Best Method for Solving a System of Equations
  • In this activity, you analyzed systems of equations and evaluated whether adding or subtracting them would allow you to solve the system. By using coefficients of variables with similar absolute values, the equations can be added or subtracted to eliminate that variable in the third equation.

After these activities, you completed the following practice:

• 2.4.5: Practice