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messersmith_power_introductory_algebra_1e_ch4_7_10

When we rewrite the equations in the form Ax By C, we get 2x 9y 4 (3) 3x 12y 7 (4) Step 2: Determine which variable to eliminate from equations (3) and (4). Often, it is easier to eliminate the variable with the smaller coeffi cients. Therefore, we will eliminate x. The least common multiple of 2 and 3 (the x-coeffi cients) is 6. Before we add the equations, one x-coeffi cient should be 6, and the other should be 6. Multiply equation (3) by 3 and equation (4) by 2. Rewrite the System 3(2x 9y) 3(4) 3 times (3) 6x 27y 12 2(3x 12y) 2(7) 2 times (4) 6x 24y 14 Step 3: Add the resulting equations to eliminate x. Solve for y. 6x 27y 12 6x 24y 14 3y 2 y 2 3 Step 4: Substitute y 2 3 into equation (1) and solve for x. 2x 9y 4 Equation (1) 2x 9 a2 3 b 4 Substitute. 2x 6 4 Multiply. 2x 10 Add. x 5 Step 5: Check to verify that a5, 2 3 b satisfi es each of the original equations. The solution is a5, 2 3 b. Once again, notice that the coefficients of x are made to be opposite in sign so that they can be eliminated when the equations are added. YOU TRY 3 Solve the system using the elimination method. 5x 2y 14 4x 3y 21 2 Solve a Linear System Using the Elimination Method: Special Cases We have seen in Sections 4.1 and 4.2 that some systems have no solution, and some have an infi nite number of solutions. How does the elimination method illustrate these results? www.mhhe.com/messersmith SECTION 4.3 Solving Systems by the Elimination Method 265


messersmith_power_introductory_algebra_1e_ch4_7_10
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