Explanation Procedure used: Solving system of linear equations by elimination: (1) If the equations are not in the standard form, they are converted accordingly into a 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) Obtain 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 been eliminated. (4) The equation in step (3) is solved to obtain the value of remaining variable. (5) The value of variable in step (4) is substituted to any 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 given equations of the system. Calculation: The given system of linear equations is: 4 x − y = 12 (1) 2 x + y = − 12 (2) Step 1: Notice that, the given equations are already in standard form. Step 2: Since the coefficients of y in the equations are additive inverses, choose the variable y for elimination. Step 3: Add the given equations to eliminate the variable y and obtain the following equation. 4 x − y = 12 2 x + y = − 12 _ 6 x = 0 Step 4: Solve the equation obtained in Step 3 to find the value of one variable. x = 0 6 = 0 Step 5: Substitute the value from Step 4 in equation (1) to obtain the value of y as follows. 4 ( 0 ) − y = 12 0 − y = 12 − y = 12 Step 6: The equation obtained in Step 5 is solved as follows. y = 12 − 1 = − 12 That is, the value of other variable is y = − 12

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

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Chapter 4, Problem 37RE

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Chapter 4, Problem 36RE

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Chapter 4 Solutions

Elementary & Intermediate Algebra

Ch. 4.1 - A _____ is a grouping of two or more linear...Ch. 4.1 - A _____ of a system of equations consists of...Ch. 4.1 - Prob. 3E Ch. 4.1 - In Problems 3 and 4, determine whether each...Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - In Problem 8, solve the system by graphing. 8....Ch. 4.1 - Prob. 9E Ch. 4.1 - If a system of linear equations in two variables...

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The system of equations { 4 x − y = 12 2 x + y = − 12 using elimination.

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