The constant on the right is divisible by the coefficients on the left, so two solutions are (x, y) = (5, 0) or (0, -3)
The slope of the line is 3/5, so increaing y by 3 and x by 5 will result in another solution. One general parametric solution is then x = 5n y = 3n-3 _____ Integer values of n will result in integer solutions. Any value of n will yield numbers that satisfy the equation.
In general, the extended Euclidean algorithm can be used to find integer solutions. Then adding multiples of some number n to y and x in the ratio of the slope of the line will yield other solutions.
