What is the number of solutions (x, y) of the equation 3x+y=100, where x and y are positive integers?

The given equation can be rewritten as y=100-3x ----- (i)

since, the minimum value of x can be 0,hence putting this value in eq (i), we get y=100 which is the maximum value of y

and minimum value of y can be 0 since it is positive integer.

hence, y is an element of [0,100] under given condition --------(ii)

now, the given equation can be rewritten as x=100-y/3-----(iii)

putting minimum and maximum value of y from eq (ii) in eq (iii) we get,

x is an element of [0,33] when x is positive integer----(iv)

from eq (ii) and eq (iv)

0 to 33 is the common value for x and y,

Hence, Number of solution for (x,y) of the equation 3x+y=100 is  34