Linear Equations

If x and y are integers, then the equation 5x + 19y = 64 has

  1. A solution for -59 < y < -56
  2. No solution for x > 250 and y > -100
  3. A solution for 250 < x < 300
  4. No solution for x < 300 and y < 0

Answer

5x + 19y = 64

If y = 1, there is an integer solution for x = 9, now if y changes (increases or decreases) by 5, then x will change (decrease or increase) by 19.

Looking at the options, if x = 256, you get y = 64.

So, there is a solution for 250 < x < 300.

The correct option is C.