EXAMPLE 4 In-Class Example 4 Solve the system using the elimination method. 4x 2y 7 3y 6x 1 Answer: Solve the system using the elimination method. 4y 10x 3 (1) 6y 15x 8 (2) Solution Step 1: Write each equation in the form Ax By C. 4y 10x 3 10x 4y 3 (3) 6y 15x 8 15x 6y 8 (4) Step 2: Determine which variable to eliminate from equations (3) and (4). Eliminate y. The least common multiple of 4 and 6, the y-coeffi cients, is 12. One y-coeffi cient must be 12, and the other must be 12. Rewrite the System 3(10x 4y) 3(3) 30x 12y 9 2(15x 6y) 2(8) 30x 12y 16 Step 3: Add the equations. 30x 12y 9 Notice that, just as in Section 4.2, if the variables drop out and you end up with a false statement, there is no solution. YOU TRY 4 Solve the system using the elimination method. 30x 12y 16 0 25 False The variables drop out, and we get a false statement. Therefore, the system is inconsistent, and the solution set is . 24x 6y 7 4y 3 16x EXAMPLE 5 In-Class Example 5 Solve the system using the elimination method. 12x 10y 6 y 6 5 x 3 5 Answer: infinite number of solutions of the form e (x, y) ` y 6 5 x 3 5 f Solve the system using the elimination method. 12x 18y 9 (1) y 2 3 x 1 2 (2) Solution Step 1: Write equation (2) in the form Ax By C. y 2 3 x 1 2 Equation (2) 6y 6 a2 3 x 1 2 b Multiply by 6 to eliminate fractions. 6y 4x 3 4x 6y 3 (3) Rewrite as Ax By C. We can rewrite y 2 3 x 1 2 as 4x 6y 3, equation (3). 266 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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