(i) x + y = 5, 2x + 2y = 10
(ii) x – y = 8, 3x – 3y = 16
Arrangements:
(i)
![\[x\text{ }+\text{ }y\text{ }=\text{ }5\text{ }and\text{ }2x\text{ }+\text{ }2y\text{ }=\text{ }10\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a7ac1456bd27f29fd042fecd333588e1_l3.png "Rendered by QuickLaTeX.com")
![\[\left( a1/a2 \right)\text{ }=\text{ }1/2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0038779ae6e92f76053812cf631b2db5_l3.png "Rendered by QuickLaTeX.com")
![\[\left( b1/b2 \right)\text{ }=\text{ }1/2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a7b518e83015c0b6a1f2eb306dc14b31_l3.png "Rendered by QuickLaTeX.com")
![\[\left( c1/c2 \right)\text{ }=\text{ }1/2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-72194260e1bef84e1b46a22add370055_l3.png "Rendered by QuickLaTeX.com")
Since
![\[\left( a1/a2 \right)\text{ }=\text{ }\left( b1/b2 \right)\text{ }=\text{ }\left( c1/c2 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-78466c740c5c43d20d1a544722f9c6f1_l3.png "Rendered by QuickLaTeX.com")
∴The conditions are incidental and they have endless number of potential arrangements.
In this way, the conditions are steady.
For,
![\[x\text{ }+\text{ }y\text{ }=\text{ }5\text{ }or\text{ }x\text{ }=\text{ }5-y\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5ff4376a2909b09b0f2bcee22f175472_l3.png "Rendered by QuickLaTeX.com")
![\[2x\text{ }+\text{ }2y\text{ }=\text{ }10\text{ }or\text{ }x\text{ }=\text{ }\left( 10-2y \right)/2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-643e83232adc1b076f6cf4877b264388_l3.png "Rendered by QuickLaTeX.com")
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,
![\[x-y\text{ }=\text{ }8\text{ }and\text{ }3x-3y\text{ }=\text{ }16\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e6cf4c70eee1cb885b8a6c60f094c636_l3.png "Rendered by QuickLaTeX.com")
![\[\left( a1/a2 \right)\text{ }=\text{ }1/3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-449d9a5633a63a197c7b2604fce9db76_l3.png "Rendered by QuickLaTeX.com")
![\[\left( b1/b2 \right)\text{ }=\text{ }-\text{ }1/\text{ }-\text{ }3\text{ }=\text{ }1/3\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-51a21d86c92732f481b18fb1025cfbb6_l3.png "Rendered by QuickLaTeX.com")
![\[\left( c1/c2 \right)\text{ }=\text{ }8/16\text{ }=\text{ }1/2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-725ba23cf12710a9a7446b694c14fe72_l3.png "Rendered by QuickLaTeX.com")
Since,
![\[\left( a1/a2 \right)\text{ }=\text{ }\left( b1/b2 \right)\text{ }\ne \text{ }\left( c1/c2 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c3e98f75f19554224e778ca550f12a31_l3.png "Rendered by QuickLaTeX.com")
The conditions are corresponding to one another and have no arrangements. Subsequently, the pair of straight conditions is conflicting.