Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 11 - Additional Topics - 11.2 - 3 x 3 Systems of Equations - Problem Set 11.2: 15

Answer

(1, 4, 2)

Work Step by Step

In order to solve systems of three linear equations, we multiply the first and second equation by values that will cancel out a variable when they are added. Thus, we multiply the first equation by 2 and the second equation by 1 and add to obtain: $8x -y =4 $ We now multiply the first and third equation by values that will cancel out a variable when they are added. Thus, we multiply the first equation by one and the third equation by 2 and add to obtain: $ 11x + y = 15 $ Plugging $y =8x -4 $ into this equation, we obtain: $ 19x - 4 = 15 \\ x= 1$ Now, we plug this value into one of the equations that only has x and y in them to find: $ y =4 $ Finally, we plug the values of x and y into the first equation listed in the book to find: $ z = 2$
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