College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 5 - Section 5.1 - Systems of Linear Equations - 5.1 Exercises - Page 487: 36

Answer

The system of equations is inconsistent and has no solutions. The lines are parallel to each other.

Work Step by Step

We need to solve the given system of equations: $$2x-3y-7=0 ~~~(1) \\ -4x+6y-14=0 ~~~(2)$$ Write each equation in standard form to obtain the equivalent system: $$2x-3y=7 ~~~(3) \\ -4x+6y=14 ~~~(4)$$ Multiply equation $(3)$ by $2$ to obtain the equivalent equation: $$4x-6y=14 ~~~~(5)$$ Add equations $(4)$ and $(5)$ to obtain: $$(-4x+6y)+(4x-6y)=14+14 \\ 0= 28 $$ Both variables were eliminated and resulted in a false equation/statement. This means that the system is inconsistent and has no solutions. This means that the lines are parallel to each other.
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