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 − 2 y = 3 (1) x − 2 y = 1 (2) Step 1: The given equations are in the required standard form, and so not required to change them. Step 2: Arbitrarily select a variable x for elimination, in the given linear system of equations. Step 3: Multiply the equation (2) by 2 and add both the equations. − 2 x − 2 y = 3 2 x − 4 y = 2 _ − 6 y = 5 That is, the equation obtained is − 6 y = 5 . Step 4: Solve the equation in Step 2 to obtain the value of variable x . − 6 y = 5 y = − 5 6 Thus, the value of y is − 5 6 . Step 5: Substitute y = − 5 6 in equation (1) to obtain the value of variable x . − 2 × ( x ) − 2 ( − 5 6 ) = 3 − 2 x = 3 − 5 3 − 2 x = 4 3 Step 6: Solve the equation obtained in Step 5 to obtain the value of variable x

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ISBN: 9780134556079

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

Publisher: Pearson,

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Chapter 4.3, Problem 30E

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To solve: The system of equations {−2x−2y=3x−2y=1 using elimination.

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Chapter 4.3, Problem 29E

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Elementary & Intermediate Algebra

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The system of equations { − 2 x − 2 y = 3 x − 2 y = 1 using elimination.

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

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To solve: The system of equations {−2x−2y=3x−2y=1 using elimination.

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