Add the equations in the rewritten system. The x is eliminated. 2x 5y 5 2x 8y 14 0x 3y 9 Add the equations. 3y 9 Simplify. y 3 Solve for y. Substitute y 3 into (1) or (2) to fi nd x. We will use equation (2). x 4y 7 Equation (2) x 4(3) 7 Substitute 3 for y. x 12 7 x 5 The solution is (5, 3). Verify that (5, 3) satisfi es equations (1) and (2). YOU TRY 2 Solve the system using the elimination method. 8x y 5 6x 2y 15 Next we summarize the steps for solving a system using the elimination method. Procedure Solving a System of Two Linear Equations by the Elimination Method Step 1: Write each equation in the form Ax By C. Step 2: Determine which variable to eliminate. If necessary, multiply one or both of the equations by a number so that the coeffi cients of the variable to be eliminated are negatives of one another. Step 3: Add the equations, and solve for the remaining variable. Step 4: Substitute the value found in Step 3 into either of the original equations to fi nd the value of the other variable. Step 5: Check the solution in each of the original equations. EXAMPLE 3 In-Class Example 3 Solve the system using the elimination method. 7y 4x 1 6x 2y 11 Answer: a 3 2 , 1b Solve the system using the elimination method. 2x 9y 4 (1) 3x 7 12y (2) Solution Step 1: Write each equation in the form Ax By C. 2x 9y 4 (1) 3x 7 12y (2) 2x 9y 4 Subtract 9y. 3x 12y 7 Subtract 12y and add 7. 264 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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