Solving Systems of Equations by Elimination – Practice Problems

Having fun while studying, practice your skills by solving these exercises!

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A system of equations, also called simultaneous equations, is two or more equations with the same variables. To determine the solution to the system, or the point where the equations intersect, there are several methods: graphing, substitution, and elimination.

This video investigates how to use elimination by addition or subtraction to solve systems of linear equations. To solve by elimination, you must manipulate the system so when adding or subtracting the equations, one of the variables will cancel out, and then you can solve for the remaining variable. After the solution for one variable is calculated, just plug the known value into one of the equations to solve for the second variable. Follow the steps you have learned to isolate the second variable by using inverse operations. Don’t forget, whatever you do to one side of the equal sign you must do to the other.

Also, remember to always check your work by plugging in the values for the variables and making sure the solutions are valid. You would hate to miss the problem because you made a careless error and complicated problems such as these have lots of room for error. There are many real world uses for solving systems of equations such as figuring out how many cupcakes and how many cookies were sold at a soccer team’s bake sale - if a certain amount of money was collected. Anytime you have a problem with the same unknowns, setting up a system of equations may be the best way to solve your problem. To learn more, watch this video.

Solve systems of equations to find solutions to problems.



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Exercises in this Practice Problem
Examine the following statements.
Describe how to solve systems of equations by elimination.
Solve the given systems of equations by elimination.
Determine how much pocket money Ben and Sam get each day.
Establish a system of equations for the given situation.
Solve the system of equations by elimination.