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 - Page 484: 8

Answer

(5, 2, -1)

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: $x + 5y =15$ 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 3 and the third equation by 1 and add to obtain: $ 5x - 3y = 19 $ Plugging $x = -5y +15$ into this equation, we obtain: $-28y + 75 = 19 \\ y =2 $ Now, we plug this value into one of the equations that only has x and y in them to find: $ x = 5$ Finally, we plug the values of x and y into the first equation listed in the book to find: $ z = -1$
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