Lesson 5: 6-5 Applying Systems of Linear Equations

If one of the variables in either equation has a coefficient of 1 or -1, what method would you use?

If one of the variables has opposite coefficients in the two equations, would you use elimination using subtraction? Explain.

If you only want to estimate the solution to a system of equations, what method would you use?

matrix
element
dimension
augmented matrix
row reduction
identity matrix

A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

SAT questions related to systems: 4-3-16,1-3-18,1-3-9,2-3-2,8-3-18,6-4-11,7-3-3,1-3-11,7-4-11,1-4-19,8-3-10,2-4-29,2-3-20,3-3-9

Different methods work better for solving certain systems of equations. Graphing can be used when an estimate will do. Substitution is used when one of the variables in either equation has a coefficient of 1 or -1. Elimination using addition or subtraction can be used if the coefficients of one of the variables are the same or additive inverses. Elimination using multiplication can be used when none of the other methods will work.

See page 370 for graph
The blue line represents the cost of renting a car from Ace Car Rental. The red line represents the cost of renting a car from Star Car Rental.
a. Write a system of linear equations based on theinformation in the graph.
b. Interpret the meaning of each equation.
c. Solve the system and describe its meaning in the context of the situation.

Students frequently do not understand what their answers mean in the context of the problem. Stress that they should go back and read the problem again to make sure they have answered the question. It is also helpful to have them give their answers to a word problem in sentence form.

If students have trouble writing the necessary equations for a system in a real-world situation,

Then give them these steps to help them explore, plan, solve, and check.

• Determine the question.

• Describe the variables used for the unknowns.

• Translate the conditions in the problem into two equations.

• Solve the system by the best method.

• Analyze the solution in the context of the situation.

Extension: Have students make up their own real-world problem that can be solved using a system of linear equations. This will help all students understand the concept of solving systems of linear equations.

Practice: Exercises 1 - 5

Exercises 29-35

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