Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.3 - More on Functions and Their Graphs - Exercise Set - Page 200: 144


The values of the required pairs are\[\left( \frac{3}{2},0 \right)\text{ and }\left( 0,-2 \right)\].

Work Step by Step

Consider the equation; $4x-3y-6=0$ The objective is to find the ordered pair $\left( \_,0 \right)\text{ and }\left( 0,\_ \right)$ that satisfies the equation $4x-3y-6=0$ Label these ordered pairs $\left( \_,0 \right)\text{ and }\left( 0,\_ \right)$ as $\left( {{x}_{1}},0 \right)\text{ and }\left( 0,{{y}_{1}} \right)$ Consider that the ordered pair satisfies the equation, then put $\left( {{x}_{1}},0 \right)$ in the equation Therefore, $\begin{align} & 4{{x}_{1}}-3\left( 0 \right)-6=0 \\ & 4{{x}_{1}}-0-6=0 \\ & {{x}_{1}}=\frac{6}{4} \\ & {{x}_{1}}=\frac{3}{2} \end{align}$ Therefore, the first ordered pair is $\left( \frac{3}{2},0 \right)$ Now put $\left( 0,{{y}_{1}} \right)$ in the equation, $\begin{align} & 4\left( 0 \right)-3{{y}_{1}}-6=0 \\ & 0-3{{y}_{1}}=6 \\ & {{y}_{1}}=-\frac{6}{3} \\ & {{y}_{1}}=-2 \end{align}$ Therefore, the required pair is $\left( 0,-2 \right)$. Hence the values of the required pairs are $\left( \frac{3}{2},0 \right)$ and $\left( 0,-2 \right)$ .
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