Explanation Procedure used: “Solving system of linear equations by elimination” (1) If the equations are not in the standard form, then they are converted accordingly into a standard form which is as follows: a x + b y = c Where x and y are variables and a , b and c are appropriate integer constants. (2) The variable to be eliminated is recognized from the given equations in the system. (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 and adding the new equations will result in a fresh equation with the decided variable to been eliminated. (4) The equation in step (3) is solved obtaining value of remaining variable. (5) The value of variable in step (4) is substituted to the equation in any of the given system equations. (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 given equations of the system. Calculation: Consider the given equations. 4 x + 3 y = 0 (1) 3 x − 5 y = 2 (2) Step 1: Both the equations (1) and (2) are already in standard form, no need to arrange in standard form. Step 2: Arbitrarily select variable x for elimination, in the given linear system of equations. Step 3: The coefficients of x in the equations are 4 and 3 , whose LCM is 12 . Thus, in order to make the coefficients of x to additive inverses, equation (1) is to be multiplied by 3 equation (2) is to be multiplied by − 4 . Since the coefficients of x became additive inverses, the equations can be added. 12 x + 9 y = 0 − 12 x + 20 y = − 8 _ 29 y = − 8 Step 4: From step 3, the value of y = − 8 29 . Step 5: Substitute y = − 8 29 in equation (1). 4 x + 3 y = 0 4 x = 0 − 3 ( − 8 29 ) 4 x = 24 29 Step 6: Solve the above equation for x

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ISBN: 9780321880116

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

Publisher: PEARSON

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Chapter 4.3, Problem 37E

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To solve: The system of linear equations 4x+3y=0 and 3x−5y=2 by elimination method.

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Chapter 4.3, Problem 36E

Chapter 4.3, Problem 38E

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Chapter 4 Solutions

Elementary & Intermediate Algebra

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The system of linear equations 4 x + 3 y = 0 and 3 x − 5 y = 2 by elimination method.

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To solve: The system of linear equations 4x+3y=0 and 3x−5y=2 by elimination method.

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