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Question

Assertion: The graph of the two linear equations x - 2y = 1 and 2x + 3y = 9 intersect at (3, 1).

Reason: Every point lying on x - 2y = 1 is a solution of 2x + 3y = 9

Now, choose the correct option.


A
Both the assertion and the reason are true and the reason is the correct explanation for the assertion.
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B
Both the assertion and the reason are true but the reason is not the correct explanation for the assertion.
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C
Assertion is true but the reason is false.
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D
If assertion is false but reason is true.
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Solution

The correct option is C Assertion is true but the reason is false.
If (3,1) lies on the graph of x-2y=1 and 2x+3y=9, then (3,1) is a solution of x - 2y =1 as well as 2x + 3y=9.

Given,x=3 and y=1

x2y=32×1=32=1

Also, 2x+3y=2×3+3×1=6+3=9

Thus, (3,1) lies on both x2y=1 and 2x+3y=9
which means x2y=1 and 2x+3y=9 intersect at (3,1)

The reason states that every point on x2y=1 lies on 2x+3y=9
(1,1) lies on x2y=1 as 12×1=1+2=1
2×1+3×1=23=59
Thus, (-1,-1) does not lie on 2x+3y=9

Hence, the reason is false.

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