Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 9 - Systems and Matrices - 9.1 Systems of Linear Equations - 9.1 Exercises - Page 857: 36

Answer

$$\emptyset ;{\text{Inconsistent System }}$$

Work Step by Step

$$\eqalign{ & \,\,\,2x - 3y - 7\,\,\,\,\, = 0\,\,\,\left( {\bf{1}} \right)\,\, \cr & - 4x + 6y - 14\,\,\, = 0\,\,\,\left( {\bf{2}} \right)\, \cr & \cr & {\text{Multiply the equation }}\left( {\bf{1}} \right){\text{ by }}2 \cr & \,\,4x - 6y - 14\,\,\,\, = 0 \cr & - 4x + 6y - 14\,\,\, = 0 \cr & {\text{Add both equations}} \cr & \,\,4x - 6y - 14\,\,\,\, = 0 \cr & \underline { - 4x + 6y - 14\,\,\, = 0} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 28 = 0\,\,\,\,\,\,\,\,\,\,\, \cr & {\text{The result}},{\text{ }} - 28 = 0,{\text{ is a false statement}},{\text{ which indicates that}} \cr & {\text{The system is inconsistent and has no solutions}}{\text{.}} \cr} $$
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