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messersmith_power_introductory_algebra_1e_ch4_7_10

Step 4: Find x by substituting 4 for y in either equation (3) or (4). Let’s use equation (4) since it has smaller coeffi cients. x 4y 10 (4) x 4(4) 10 Substitute. x 16 10 Multiply. x 6 Subtract 16 from each side. x 6 Divide by 1. Step 5: Check x 6 and y 4 in the original equations. The solution of the system is (6, 4). YOU TRY 2 Solve each system by the substitution method. a) 1 6 x 1 3 y 2 3 b) 0.1x 0.03y 0.05 3 2 x 0.1x 0.1y 0.6 5 2 y 7 3 Solve a System by Substitution: Special Cases We saw in Section 4.1 that a system may have no solution or an infi nite number of solutions. If we are solving a system by graphing, we know that a system has no solution if the lines are parallel, and a system has an infi nite number of solutions if the graphs are the same line. When we solve a system by substitution, how do we know whether the system is inconsistent or dependent? Read Examples 4 and 5 to fi nd out. EXAMPLE 4 In-Class Example 4 Solve the system by substitution. 2x y 3 6x 3y 0 Answer: Solve the system by substitution. 3x y 5 (1) 12x 4y 7 (2) Solution Step 1: y 3x 5 Solve equation (1) for y. Step 2: 12x 4y 7 Substitute 3x 5 for y in equation (2). 12x 4(3x 5) 7 Step 3: 12x 4(3x 5) 7 Solve the resulting equation for x. 12x 12x 20 7 Distribute. 20 7 False Because the variables drop out and we get a false statement, there is no solution to the system. The system is inconsistent, so the solution set is . Remember that a system of linear equations has no solution when the two lines are parallel. x y 5 3x y 5 12x 4y 7 5 5 5 The graph of the equations in the system supports our work. The lines are parallel; therefore, the system has no solution. 258 CHAPTER 4 Linear Equations and Inequalities in Two Variables www.mhhe.com/messersmith


messersmith_power_introductory_algebra_1e_ch4_7_10
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