find all the positive integer solutions to 17x + 11y =120?

Answer 1

Since 120 / 17 is 7.058..., x can only be 1, 2, 3, 4, 5, or 6.

Try each one, multiply it by 17, subtract this from 120, then divide by 11 to see if it comes out an integer.

Answer 2

Write out multiples of 17 ( 17, 34, .. 119) and eleven (11,22 .. 110)

Since the sum is even, you only need compare odd multiples of 11 and odd multiples of 17 OR even multiples of 11 with even multples of 17.

I don't think there are solutions. But try it out.