Explanation Procedure used: Solving system of linear equations by elimination: (1) If the equations are not in the standard form, convert into the standard form a x + b y = c , where x and y are variables and a , b and c are appropriate constants greater than one. (2) The variable to be eliminated is recognized from the given system of equations. (3) After obtaining the LCM (lowest common multiple) of coefficients of the variable to be eliminated, the equations are multiplied with appropriate multipliers so that the coefficients in each equation become additive inverses. Adding the new equations will result in a fresh equation with the decided variable to be eliminated. (4) The equation in step (3) is solved to obtain value of the remaining variable. (5) The value of the variable in step (4) is substituted to any one of the equation in the given system. (6) Solving the equation obtained in step (5) gives the value of variable eliminated in step (3). (7) The correctness of solution is asserted by substituting back the values in the given system of equations. Calculation: The given equations are: 2 x + y = − 4 (1) 3 x + 5 y = 29 (2) Step 1: The given equations are in the required standard form, and so not required to change them. Step 2: The variable to be eliminated is arbitrarily chosen as x . Step 3: The LCM of the coefficients of x is 6. Multiply the equation ( 1 ) by –3 and equation ( 2 ) by 2 and add the resultant equations. − 6 x − 3 y = 12 6 x + 10 y = 58 _ 7 y = 70 That is, the equation obtained is 7 y = 70 . Step 4: Solve the equation in Step 2 to obtain the value of variable x . 7 y = 70 y = 10 Step 5: Substitute the value of x in equation (1) to obtain the value of variable y . 2 x + 10 = − 4 2 x = − 14 Step 6: Solve the equation obtained in Step 5 to obtain the value of variable x . 2 x = − 14 x = − 7 Step 7: Substitute x = − 7 and y = 10 in equation 2 x + y = − 4

3rd Edition

ISBN: 9780321880116

Author: Michael Sullivan III, Katherine R. Struve, Janet Mazzarella

Publisher: PEARSON

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Chapter 4.3, Problem 28E

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To solve: The system of equations {2x+y=−43x+5y=29 using elimination.

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Chapter 4.3, Problem 27E

Chapter 4.3, Problem 29E

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Chapter 4 Solutions

Elementary & Intermediate Algebra

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The system of equations { 2 x + y = − 4 3 x + 5 y = 29 using elimination.

Solution Summary: The author explains how to solve the system of linear equations by elimination.

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To solve: The system of equations {2x+y=−43x+5y=29 using elimination.

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