Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 3 - Section 3.1 - Systems of Linear Equations in Two Variables - Exercise Set - Page 190: 24

Answer

No solution.

Work Step by Step

First equation $2x-3y=6$. Plug $y=0$ into the equation. $\Rightarrow 2x-3(0)=6$ $\Rightarrow 2x=6$ $\Rightarrow \frac{2x}{2}=\frac{6}{2}$ $\Rightarrow x=3$ $x−$ intercept $A=(3,0)$. Plug $x=0$ into the equation. $\Rightarrow 2(0)-3y=6$ $\Rightarrow -3y=6$ $\Rightarrow \frac{-3y}{-3}=\frac{6}{-3}$ $\Rightarrow y=-2$ $y−$ intercept $B=(0,-2)$. Second equation $4x-6y=24$. Plug $y=0$ into the equation. $\Rightarrow 4x-6(0)=24$ $\Rightarrow 4x=24$ $\Rightarrow \frac{4x}{4}=\frac{24}{4}$ $\Rightarrow x=6$ $x−$ intercept $A=(6,0)$. Plug $x=0$ into the equation. $\Rightarrow 4(0)-6y=24$ $\Rightarrow -6y=24$ $\Rightarrow \frac{-6y}{-6}=\frac{24}{-6}$ $\Rightarrow y=-4$ $y−$ intercept $B=(0,-4)$. Draw two lines using intercept points. Both lines are parallel. Hence, we have no solution.
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