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Question

The equation 2x+5y=7has a unique solution, if x,y are


A

Natural numbers

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B

Positive real numbers

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C

Real numbers

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D

Rational numbers

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Solution

The correct option is A

Natural numbers


Consider, 2x+5y=7

A. (1,1) is a solution of 2x+5y=7

B. If positive real numbers are chosen, 2x+5y=7 will have many solutions.

C. If real numbers are chosen, 2x+5y=7 will have infinite solutions.

D. If rational numbers are chosen, 2x+5y=7 will have many solutions.

A linear equation in two variables has infinitely many solutions. For the linear equations system, there is a solution set of infinite points for which the L.H.S of an equation becomes R.H.S.

Therefore, for the unique solution of the given equation, the values will be a natural number.

Therefore, the correct option is A.


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