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: 13

Answer

(3, 0, -2)

Work Step by Step

In order to solve systems of three linear equations, we 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 1 and the third equation by -4 and add to obtain: $-7x -17y = -21 $ We now 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 one and the second equation by two and add to obtain: $ 7x + y = 21 $ Plugging $7x =-17y + 21$ into this equation, we obtain: $-16y +21 = 21 \\ y = 0 $ Now, we plug this value into one of the equations that only has x and y in them to find: $ x = 3$ 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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