Explanation Given information: The system of equation as below: 0.3 x + 0.2 y = 5 0.5 x + 0.4 y = 11 Formula used: By the addition principle, for any real numbers a , b and c with c ≠ 0 a = b is equivalent to a + c = b + c . Do the following steps to solve the system of equations by elimination method. Step 1: Write the equation in A x + B y = C form. Step 2: Clear the fractions or decimals from the equation. Step 3: Multiply one or both equations by a non-zero constant (if required) to create opposite coefficient for one of the variables and add/subtract the equation to eliminate one variable. Step 4: Solve the other remaining variable. Step 5: Solve the other variable. Step 6: Check the solution. Calculation: Consider the system of equation and mark them with (1) and (2) for further reference as below: 0.3 x + 0.2 y = 5 …… (1) 0.5 x + 0.4 y = 11 …… (2) Make the coefficients opposites of each other and not in the decimal form, so that one of them can be eliminated. Multiply equation (1) by − 50 0.3 x + 0.2 y = 5 − 50 ( 0.3 x + 0.2 y ) = − 50 ( 5 ) − 15 x − 10 y = − 250 Then, equation (1) is transformed as below: − 15 x − 10 y = − 250 …… (3) To make the coefficients opposites of each other, so that one of them can be eliminated, multiply equation (2) by 30 0.5 x + 0.4 y = 11 30 ( 0.5 x + 0.4 y ) = 30 ( 11 ) 15 x + 12 y = 330 Then, equation (2) is transformed as below: 15 x + 12 y = 330 …… (4) The coefficient of x is opposite in both the equation (3) and (4) Add the equations (3) and (4) to eliminate one variable, − 15 x − 10 y = − 250 15 x + 12 y = 330 _ 2 y = 80 Further solve and get, 2 y = 80 y = 40 Substitute the value of y in any of the equations, here equation (4) and solve for the value of x as below: 15 x + 12 y = 330 15 x + 12 ( 40 ) = 330 15 x + 480 = 330 x = − 10 Then the values are x = − 10 and y = 40

Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)

7th Edition

ISBN: 9780134462707

Author: Marvin L. Bittinger, David J. Ellenbogen, Barbara L. Johnson

Publisher: PEARSON

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Chapter 8.2, Problem 46ES

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To calculate: The solution for the system of equations 0.3x+0.2y=5, 0.5x+0.4y=11 by the elimination method.

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Chapter 8.2, Problem 45ES

Chapter 8.2, Problem 47ES

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Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)

Ch. 8.1 - In 2016, there were 35 species of amphibians in...Ch. 8.1 - 2. Refer to Example 2 . For another necklace, Star...Ch. 8.1 - Prob. 3YT Ch. 8.1 - Prob. 4YT Ch. 8.1 - Prob. 1CYU Ch. 8.1 - Prob. 2CYU Ch. 8.1 - Prob. 3CYU Ch. 8.1 - Prob. 4CYU Ch. 8.1 - Prob. 1ES Ch. 8.1 - Prob. 2ES

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The solution for the system of equations 0.3 x + 0.2 y = 5 , 0.5 x + 0.4 y = 11 by the elimination method.

Solution Summary: The author explains how to solve the system of equations by the elimination method by writing the equation in Ax+By=C form.

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To calculate: The solution for the system of equations 0.3x+0.2y=5, 0.5x+0.4y=11 by the elimination method.

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Chapter 8 Solutions