Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 4 - Section 4.2 - Solving Systems of Linear Equations in Three Variables - Exercise Set - Page 220: 9

Answer

No Solution.

Work Step by Step

$4x-y+2z=5$ Equation $(1)$ $2y+z=4 $ Equation $(2)$ $4x+y+3z=10$ Equation $(3)$ Multiply Equation $(1)$ by $2$ then add with Equation $(2)$ to eliminate $y$ $2(4x-y+2z)+2y+z=2(5)+4 $ $8x-2y+4z+2y+z=10+4 $ Combine like terms. $8x+5z=14$ Equation $(4)$ Multiply Equation $(3)$ by $-2$ then add with Equation $(2)$ to eliminate $y$ $-2(4x+y+3z)+2y+z=-2(10)+4 $ $-8x-2y-6z+2y+z=-20+4 $ Combine like terms. $-8x-5z=-16$ Equation $(5)$ Add Equation $(4)$ and Equation $(5)$ $8x+5z-8x-5z=14-16$ $0=-2$ Since the statement is not true, this system is inconsistent and has no solution.
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