Solving Systems of Equations by Substitution – Practice Problems

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

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Do you need help? Watch the Video Lesson for this Practice Problem. Solving Systems of Equations by Substitution

Systems of equations, also called simultaneous equations, are problems with two or more equations having 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 substitution to solve systems of linear equations. To solve using substitution for a system with two equations, you must find the value of one of the variables in terms of the other and substitute it into one of the equations, allowing you to know the value for one of the variables. Next, substitute the value of that variable into the other equation and solve for the second variable. After you know the solution for both variables, plug them back into the system to verify they work.

There are a lot of steps to solving this type of problem, and you know what they say: the more the steps, the greater the chance of making a silly mistake. But keep in mind, if you get a funny answer, it could be that there is no solution, or the entire line could be the solution. If this process of solving systems of equations with substitution seems confusing, then you had better watch this video, so you can see an example worked out and have a great time while you do.

Solve systems of equations to find solutions to problems.

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Exercises in this Practice Problem
Explain how to solve a system of equations by substitution.
Determine the number of long-haired and short-haired cats by substitution.
Decide how many dogs Miss Lovingdogs can bring to the dog stylist.
Write a system of equations for each situation and solve them.
Determine the two equations that are needed to correctly describe Miss Anderson's problem.
Solve the system of equations.