Solving systems of equations graphically
Graphing systems of equations 256
Exercise Name: Solving systems of equations graphically
Math Missions: 8th grade (U.S.) Math Mission, Algebra basics Math MissionAlgebra I Math Mission, Algebra II Math Mission, Mathematics III Math Mission
Types of Problems: 1

The Solving systems of equations graphically exercise appears under the 8th grade (U.S.) Math Mission, Algebra basics Math MissionAlgebra I Math Mission, Algebra II Math Mission and Mathematics III Math Mission. This exercise draws systems of equations on the coordinate plane and uses the picture to find the solution.

Types of Problems

There is one type of problem in this exercise:

  1. Graph the lines and find the intersection: This problem provides a Cartesian coordinate plan and a couple equations of lines. The user is asked to draw the lines on the plan, and give the solution to the system.

    Graph the lines and find the intersection


Necessary skills include an ability to graph lines. Other skills, such as solving system of equations, are useful but not necessary.

  1. The solution to a system of equations is the point where the lines intersect.
  2. The manipulative is straight-forward to use and the lines are color-coded.
  3. The point of intersection will always be integral (both coordinates will be integers) so if the point is in between grid points and error has occurred.
  4. There is no need to solve the system separately, the graph should yield the solution if done correctly.
  5. The lines are given in slope-intercept form, so one method to graph would be to place one point at the y-intercept, then use the rise over run of the slope to get a second point.
  6. An ordered pair {(x,y)} is a solution of the system only when it is a solution of each of the given equations.

Real-life applications

  1. Applications include supply and demand lines form business and various other situations where there is information gained from different resources.
  2. Equations show up in nearly every science or business class one is ever in.
  3. Computers are also equation solvers. Computers were originally invented to solve equations over and over again instead of humans doing the calculations.
  4. Knowledge of algebra is essential for higher math levels like trigonometry and calculus. Algebra also has countless applications in the real world.

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