Answer
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 $\left( 0,-2 \right)$ .