Objective: Solve application problems using systems of two linear equations.
A system of equations can be a powerful tool for solving application problems. In order to correctly solve application problems and clearly communicate the process, use the following four steps:
1. Define your variables. Determine what you are trying to solve for and define what your variables stand for in each problem.
2. Translate into a system of equations. Use the information in the word problem to write two equations with two variables.
3. Solve the system. Use any of the methods described in the previous lessons.
4. Clearly state and label your answer. Remember that solving the system is not the same thing as fully answering the question(s) posed by the word problem. Make sure you do this final step.
A problem involving a mixture of two things can be solved using a system of two linear equations. Watch the video below to see some examples of how to set up a system of equations for a mixture problem.
If you want to see how the answers to the mixture problems shown in the above video were arrived at by using the substitution method or the elimination method, watch the video below.
Complete the worksheet attachment below and then check your answers using the solutions attachment. Once you have completed these exercises, click the link to advance to the next lesson.