Question

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

• A. Natural numbers
• B. Positive real numbers
• C. Real numbers
• D. Rational numbers

Answer 1

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.