(i) x + y = 5, 2x + 2y = 10
(ii) x – y = 8, 3x – 3y = 16
Arrangements:
(i)
\[x\text{ }+\text{ }y\text{ }=\text{ }5\text{ }and\text{ }2x\text{ }+\text{ }2y\text{ }=\text{ }10\]
\[\left( a1/a2 \right)\text{ }=\text{ }1/2\]
\[\left( b1/b2 \right)\text{ }=\text{ }1/2\]
\[\left( c1/c2 \right)\text{ }=\text{ }1/2\]
Since
\[\left( a1/a2 \right)\text{ }=\text{ }\left( b1/b2 \right)\text{ }=\text{ }\left( c1/c2 \right)\]
∴The conditions are incidental and they have endless number of potential arrangements.
In this way, the conditions are steady.
For,
\[x\text{ }+\text{ }y\text{ }=\text{ }5\text{ }or\text{ }x\text{ }=\text{ }5-y\]
\[2x\text{ }+\text{ }2y\text{ }=\text{ }10\text{ }or\text{ }x\text{ }=\text{ }\left( 10-2y \right)/2\]
In this way, the conditions are addressed in charts as follows:
From the figure, we can see, that the lines are covering one another.
Subsequently, the conditions have boundless potential arrangements.
(ii)
Given,
\[x-y\text{ }=\text{ }8\text{ }and\text{ }3x-3y\text{ }=\text{ }16\]
\[\left( a1/a2 \right)\text{ }=\text{ }1/3\]
\[\left( b1/b2 \right)\text{ }=\text{ }-\text{ }1/\text{ }-\text{ }3\text{ }=\text{ }1/3\]
\[\left( c1/c2 \right)\text{ }=\text{ }8/16\text{ }=\text{ }1/2\]
Since,
\[\left( a1/a2 \right)\text{ }=\text{ }\left( b1/b2 \right)\text{ }\ne \text{ }\left( c1/c2 \right)\]
The conditions are corresponding to one another and have no arrangements. Subsequently, the pair of straight conditions is conflicting.