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Q. 45

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Precalculus Enhanced with Graphing Utilities

Found in: Page 714

Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Solve each system of equations. If the system has no solution, say that it is inconsistent.
$x - y - z = 1 2 x + 3 y + z = 2 3 x + 2 y = 0$

The system is inconsistent

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given information

We are given a system of equation as

$x - y - z = 1 (1) 2 x + 3 y + z = 2 (2) 3 x + 2 y = 0 (3)$

Step 2: Add equation 1 and 2

We get,

$x - y - z = 1 + 2 z + 3 y + z = 2 3 x + 2 y = 3$

But from equation 3 we have $3 x + 2 y = 0$

As same equation cannot have different values

Hence the system is inconsisitent

Step 3: Conclusion

The given system of equation is inconsistant

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