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Question

If 2a=b, the pair of equations x+2y=2a−6b,ax+by=2a2−3b2 possess _____ solution(s)

A
No
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B
Only one
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C
Only two
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D
An infinite number of slutions
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Solution

The correct option is D An infinite number of slutions
Given 2a=ba=b2

x+2y=2a6b [first given equation]
x+2y=b6b=5b ........eq(i)
ax+by=2a23b2 [second given equation]
b2x+by=2b243b2
bx2+by=5b22
bx+2by=5b2 ..........eq(ii)

From (i) and (ii), Both represents same equations.
So there exits infinite number of solutions.

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