Given,
\[2x\text{ }+\text{ }y-6\text{ }=\text{ }0\text{ }and\text{ }4x-2y-4\text{ }=\text{ }0\]
$\left( a1/a2 \right)\text{ }=\text{ }2/4\text{ }=\text{ }1/2$
$\left( b1/b2 \right)\text{ }=\text{ }1/\text{ }-\text{ }2$
\[\left( c1/c2 \right)\text{ }=\text{ }-\text{ }6/\text{ }-\text{ }4\text{ }=\text{ }3/2\]
Since,
\[\left( a1/a2 \right)\text{ }\ne \text{ }\left( b1/b2 \right)\]
The given direct conditions are meeting each other at one point and have just a single arrangement. Subsequently, the pair of direct conditions is steady.
Presently, for
\[2x\text{ }+\text{ }y-6\text{ }=\text{ }0\text{ }or\text{ }y\text{ }=\text{ }6-2x\]
Furthermore, for
\[4x-2y-4\text{ }=\text{ }0\text{ }or\text{ }y\text{ }=\text{ }\left( 4x-4 \right)/2\]
In this way, the conditions are addressed in charts as follows:
From the diagram, it tends to be seen that these lines are converging each other at only one point, \[\left( 2,2 \right)\] .
(ii)
Given,
\[2x-2y-2\text{ }=\text{ }0\text{ }and\text{ }4x-4y-5\text{ }=\text{ }0\]
\[\left( a1/a2 \right)\text{ }=\text{ }2/4\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\]
\[\left( b1/b2 \right)\text{ }=\text{ }-\text{ }2/\text{ }-\text{ }4\text{ }=\text{ }1/2\]
\[\left( c1/c2 \right)\text{ }=\text{ }2/5\]
Since,
$a1/a2\text{ }=\text{ }b1/b2\text{ }\ne \text{ }c1/c2$
Hence, these straight conditions have resemble and have no potential arrangements. Subsequently, the pair of direct conditions are conflicting.