Section 3.4 Solving Systems of Linear Equations in Two Variables by the Substitution Method.

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Section 3.4 Solving Systems of Linear Equations in Two Variables by the Substitution Method

3.4 Lecture Guide: Solving Systems of Linear Equations in Two Variables by the Substitution Method Objective 1: Solve a system of linear equations by the substitution method.

Substitution Method Step 1. Solve one of the equations for one ____________ in terms of the other ____________. Example:

Step 2. ____________ the expression obtained in Step 1 into the other equation (eliminating one of the variables), and solve the resulting equation. Substitution Method

Step 3. Substitute the ____________ obtained in Step 2 into the equation obtained in Step 1 (back-substitution) to find the value of the other variable. Substitution Method The ordered pair obtained in Steps 2 and 3 is the solution that should check in both equations.

Solve each system using the substitution method. 1.

Solve each system using the substitution method. 2.

Solve each system using the substitution method. 3.

4. Solve each system using the substitution method.

5.

Solve each system using the substitution method. 6.

7. To review the three possible cases for systems of two linear equations in two variables, match each sentence with the case it describes. a. Consistent system of independent equations. ______ b. Inconsistent system. ______ c. Consistent system of dependent equations. ______ A. The solution process will produce unique x- and y-values. B. The solution process will produce an identity. C. The solution process will produce a contradiction.

8. The costs for renting a rug-shampooing machine from two different rental companies are given by the graphs shown below. The graph of gives the cost by Dependable Rental Company based upon the number of hours of use. The graph of gives the cost by Anytime Rental Company based upon the number of hours of use. $ Cost Hours

8 (a) Use the y-intercept and an additional point to determine the equation of the line for the Dependable Rental Company. $ Cost Hours

8 (b) Use the y-intercept and an additional point to determine the equation of the line for the Anytime Rental Company. $ Cost Hours

8 (c) Solve the system of equations using the substitution method. $ Cost Hours

8 (d) Interpret the meaning of the x- and y-coordinates of this solution. $ Cost Hours