For what natural number of x and y the equation 2x+5y-7=0 has unique solutions? If the values are taken from collection of real numbers do you think the equation has unique solution

Answer 1

clearly, x=1 and y=1 is a solution.
It is clearly the only solution, since using any other natural numbers (which are positive integers) produces 2x+5y which is greater than 7.

If you include all real numbers, the graph is a line, and any point on the line is a solution. It happens that the only point with positive integer coefficients is (1,1).