Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 3 - Section 3.1 - Systems of Two Equations in Two Unknowns - Exercises - Page 185: 13

Answer

There is no real solution to the system of equations. It is inconsistent. On the graph, the lines don't intersect.

Work Step by Step

1) $2x+3y=2$ 2) $-x-\frac{3y}{2}=-\frac{1}{2}$ If we multiply the second equation by 2, eliminating the fractions, we get: 2) $2\times(-x-\frac{3y}{2})=2\times(-\frac{1}{2})$ 2) $-2x-3y=-1$ In order to solve the system of equations, we can now add equation 1) to equation 2): 0=1 This means that the system of equations is inconsistent; there is no real solution to it. Graphing both equations, we can observe that they don't intersect. See the picture attached. The function between x and y can be given by solving any of the two equations: 1) $2x-3y=1$ $2x=1+3y$ $x=\frac{1+3y}{2}$ By graphing both equations we expect to have only one line on the graph. See the picture attached.
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