Education Technology

Systems of Equations

Activity Overview

In this activity, students will recognize a system of equations, determine solutions graphically, and verify solutions algebraically.


  • Students will recognize a system of equations.
  • Students will know the definition of a system of an equation.
  • Students will determine solutions to a system of equations graphically.
  • Students will verify solutions to a system algebraically.
  • Students will understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
  • Students will solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations.


  • System of Equations
  • Solving a System of Equations
  • Point of Intersection
  • Parallel lines
  • Variables

About the Lesson

This lesson involves definitions of a system of equations and solutions to a system of equations.
As a result, students will:

  • Examine a graph of a system of two equations and two unknowns. They will be able to drag a point along the x-axis and as they do, corresponding points will move along the two graphs of the equations.
  • Recall that any point on a particular equation is a solution to that given equation, but should notice that to solve a system of equations, they are looking for a solution that simultaneously solves both equations.