Course Glossary

Solving Systems of Linear Equations

Students doing homework together in a library

problem set iconUsing your knowledge of solving systems of linear equations, solve each problem shown below. Follow the instructions for each problem, answer all of the questions, and make sure to show all of your work.

This activity is available below or in a printable document.

  1. Solve the following systems of linear equations by elimination.

    A)   2 x plus y equals 6; 3 x plus 2 y equals 12

    B)   4 x plus 5 y equals 40; 5 x plus 4 y equals 5

  2. Solve the following systems of linear equations by substitution.

    A)   x equals the fraction 1 over 3 multipled by y; y minus 3 x equals 0

    B)   3 x minus y equals 1; 2 x minus 2 y equals 6

  3. Solve for the following systems of linear equations by graphing. Provide a rough sketch of the graph of each system.

    A)   y equals the fraction negative 1 over 3 multipled by x plus 4; y equals the fraction 1 over 2 multipled by x minus 5

    B)   negative 4 x plus 3 y equals negative 12; y eqauls 2 x minus 10

  4. Solve the following system of linear equations by substitution. Then, confirm your answer by graphing the system.

    y equals the fraction negative 5 over 2 multiplied by x plus 7; 5 x plus 2 y equals negative 14

  5. How does the graph of a system of linear equations with one solution differ from the graph of a system of linear equations with infinite solutions?

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