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Question

Determine how many solution exist for the following pair of equations 8x+5y=9,16x+10y=27

A
Both equations form coincident line hence they have no solutions.
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B
Both equations form parallel lines hence they have no solutions.
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C
Both equations form intersecting lines hence they have no solutions.
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D
None of these
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Solution

The correct option is B Both equations form parallel lines hence they have no solutions.
The following pair of equations can be written as

8x+5y9=0 ;16x+10y27=0;

Here a1a2=816=12

b1b2=510=12

c1c2=927=13,

We can see a1a2=b1b2c1c2

Hence, the given pair of the linear equation is inconsistent and has no solution.

For a graphical solution,

8x+5y=9

y=98x5

16x+10y=27

y=2716x10

Now, we can make the table and make the graph as shown in the solution.

357105_232413_ans_8f37a084dd144fdb9f1931af411e38aa.png

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