Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 10 - Section 10.2 - Systems of Linear Equations in Several Variables - 10.2 Exercises - Page 697: 31

Answer

Inconsistent.

Work Step by Step

Express x from the second equation. $2x+3y-z=1$ $x+2y=3 \rightarrow x=-2y+3$ $x+3y+z=4$ Substitute $ x=-2y+3$ into the first and the third equation. $2(-2y+3)+3y-z=1$ $-2y+3+3y+z=4$ Simplify. $-y-z=-5$ $y+z=1$ Add the equations. $0=-4$ After addition of the equations we got that $0=-4$ which is false. No values of x, y and z satisfy this equation and therefore the system is inconsistent.
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