2.7.6 Lesson Summary

In this lesson, you learned how to:

• Determine how many solutions a system of equations could have.

Here are the activities that helped you reach those goals:

• 2.7.1: Systems of Linear Equations with Infinitely Many Solutions
  • In this activity, you analyzed a system of equations that has infinitely many solutions. When solving by graphing, the graphs of the equations are the same line. When solving by substitution or elimination, you end up with an equation, such as $4x=4x$, that is always true no matter what value is used.
• 2.7.2: Systems of Linear Equations with No Solution
  • In this activity, you analyzed a system of equations that has no solution. This means there are no values that make both equations in the system true. When solving by graphing, the graphs of the equations are parallel lines that never intersect. When solving by substitution or elimination, you end up with an equation, such as $0=24$, that is never true.
  • 2.7.2: Self Check
  • 2.7.2: Additional Resources
• 2.7.3: Sorting Systems of Equations Based on Number of Solutions
  • In this activity, you solved many different systems of equations in order to sort which systems had one solution, infinitely many solutions, or no solution.
  • 2.7.3: Self Check
  • 2.7.3: Additional Resources
• 2.7.4: Writing Consistent and Inconsistent Systems of Equations
  • In this activity, you wrote new systems of equations to have one solution, infinitely many solutions, or no solution. By writing new systems of equations from each category, you demonstrated an awareness of the characteristics of each type of system.

After these activities, you completed the following practice:

• 2.7.5: Practice