Explanation Given: The given system of equation is, 11 x + 17 y − 13 z = − 186 12 x + 32 y + 64 z = − 92 15 x − 41 y + 88 z = 1132 Approach: The procedure to solve a given system of equation using elimination method is as follows: Step 1 : Combine two equations so that one variable is eliminated. Step 2 : Combine two different equations so that the same variable is eliminated. Step 3 : Steps 1 and 2 result in a system of two equations in two unknowns. Solve that system with the elimination method. Step 4 : Substitute back into various equations to find the values of the remaining variables. Step 5 : Check the answer by substituting it into the original equations. Calculation: Consider the given equations: 11 x + 17 y − 13 z = − 186 …… ( 1 ) 12 x + 32 y + 64 z = − 92 …… ( 2 ) 15 x − 41 y + 88 z = 1132 ..…. ( 3 ) Multiply equation ( 1 ) by 16 and equation ( 2 ) by 13 and add the resultant equation to eliminate z . 176 x + 272 y = − 2976 + 39 x + 104 y + 208 z = − 299 _ 215 x + 376 y = − 3275 …… ( 4 ) Multiply equation ( 1 ) by 88 and equation ( 3 ) by 13 and add the resultant equation to eliminate z . 968 x + 1496 y − 1144 z = − 16368 + 195 x − 533 y + 1144 z = 14716 _ 1163 x + 963 y = − 1652 …… ( 5 ) Multiply equation ( 4 ) by 963 and equation ( 5 ) by − 376 and add the resultant to eliminate y . 207045 + 381348 y = − 3153852 − 437288 x − 381348 y = 621152 _ − 230243 x = − 2532673 Solve for x . x = − 2532673 − 230243 = 11 Substitute 11 for x in equation ( 4 ) to solve for y . 215 ( 11 ) + 376 y = − 3275 y = − 3275 − 2365 376 = − 15 Substitute 11 for x and − 15 for y in equation ( 1 ) to solve for z

MATHEMATICS A PRACTICAL ODYSSEY W/ACCESS

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ISBN: 9780357537343

Author: Johnson

Publisher: CENGAGE L

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Chapter 11.4, Problem 10E

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MATHEMATICS A PRACTICAL ODYSSEY W/ACCESS

Ch. 11.0A - In Exercises 1-10, a find the dimensions of the...Ch. 11.0A - Prob. 2E Ch. 11.0A - Prob. 3E Ch. 11.0A - Prob. 4E Ch. 11.0A - Prob. 5E Ch. 11.0A - Prob. 6E Ch. 11.0A - Prob. 7E Ch. 11.0A - Prob. 8E Ch. 11.0A - Prob. 9E Ch. 11.0A - In Exercises 1-10, a find the dimensions of the...

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Chapter 11 Solutions

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The solution of the system of equations with elimination method.