To determine To solve: The system of linear equations 3 x + 5 y = − 2 and 9 x + 15 y = − 6 by elimination method. Explanation Given: The provided system of linear equations is { 3 x + 5 y = − 2 9 x + 15 y = − 6 . 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. (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. 3 x + 5 y = − 2 (1) 9 x + 15 y = − 6 (2) Step 1: Skip Step 1 as the equations (1) and (2) are already in standard form. Step 2: The coefficient of x in equation (1) is 3 and that in equation (2) is 9. Coefficient of y in equation (1) is 5 and that in equation (2). So, x or y either of the two can be a better choice of variable to be eliminated. Step 3: Multiply equation (1) by 3 which gives the equation as follows: 9 x + 15 y = − 6 (3) Step 4: Subtract equation (2) from equation (3). 9 x + 15 y = − 6 − 9 x − 15 y = 6 _ 0 = 0 Since the above equation is a true statement, therefore the solution for the given system of equations is infinite. The value of x is − 2 − 5 y 3 Step 5: It is observed that the given system of equations has infinite number of solutions, therefore skip Step 5 and Step 6. Step 7: The obtained order pair of solution is ( − 2 − 5 y 3 , y ) . Now to obtain particular solution consider y as 2 which implies x as − 4 . Therefore one of the particular solution is ( − 4 , 2 ) . Check whether the obtained order pair satisfies the given equations or not. Replace variable x with − 4 and variable y with 2 in equation (1)

6th Edition

ISBN: 9780321900760

Author: Rockswold

Publisher: PEARSON EDUCATION (COLLEGE)

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Chapter 6.1, Problem 40E

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To solve: The system of linear equations 3x+5y=−2 and 9x+15y=−6 by elimination method.

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Chapter 6.1, Problem 39E

Chapter 6.1, Problem 41E

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Ch. 6.1 - CHECKING ANALYTIC SKILLS Use each graph to...Ch. 6.1 - Prob. 8E Ch. 6.1 - CHECKING ANALYTIC SKILLS Use each graph to...Ch. 6.1 - Prob. 10E Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E

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