Question

The equation 2x + 5y = 7 has a unique solution, if x and y are
(a) natural numbers
(b) rational numbers
(c) positive real numbers
(d) real numbers

Answer 1

Since, every point on the line represented by the equation 2x + 5y = 7 is its solution.

Therefore, there are infinite solutions of the equation the equation 2x + 5y = 7 in which the values of x and y are rational numbers, positive real numbers or real numbers.

But, as 2 + 5 = 7, i.e. x = 1 and y = 1 are the only pair of natural numbers that are the solution of the equation the equation 2x + 5y = 7.

So, the equation 2x + 5y = 7 has a unique solution, if x and y are both are natural numbers.

Hence, the correct option is (a).