Explanation Given: The given system of equation is, 2 x + 2 y + z = 5 3 x − y = 5 2 y + 7 z = − 9 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: 2 x + 2 y + z = 5 …… ( 1 ) 3 x − y = 5 …… ( 2 ) 2 y + 7 z = − 9 ..…. ( 3 ) Multiply equation ( 1 ) by − 7 and add the resulting equation with equation ( 3 ) to eliminate z . − 14 x − 14 y − 7 z = − 35 + 2 y + 7 z = − 9 _ − 14 x − 12 y = − 44 …… ( 4 ) Multiply equation ( 2 ) by 5 and then add the resultant equation with equation ( 4 ) to eliminate y . − 36 x + 12 y = − 60 − 14 x − 12 y = − 44 _ − 50 x = − 104 Solve for x . x = − 104 − 50 = 52 25 Substitute 52 25 for x in equation ( 2 ) to solve for y . 3 ( 52 25 ) − y = 5 y = 156 25 − 5 = 156 − 125 25 = 31 25 Substitute 31 25 for y in equation ( 3 ) to solve for z . 2 ( 31 25 ) + 7 z = − 9 7 z = − 9 − 62 25 z = − 262 7 ( 25 ) = − 41 25 Therefore, the solution of the system of equation is ( x , y , z ) = ( 52 25 , 31 25 , − 41 25 )

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 6E

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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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Solution Summary: The author explains the procedure to solve a given system of equations using elimination method.

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Chapter 11 Solutions

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The solution of the system of equations with elimination method.