How many integer values of x and y are there such that 4x + 7y= 3 , while |x|<500 and |y|<500 ?

Question

How many integer solutions are there to the system of equations below and which are those solutions?

x^2+y-z = 42
x+y^2-z = 18

Answer 1

possible solution of 4x + 7y = 3 -500<= x <= 500 , -500 <=y <= 500

are x=6 , y= -3
x=13 , y=-7

   x=-1 , y= 1

 x= -8   y=5

so x has a gap of 7 units 497/7 = 71 ,, so last term is - 498 ,, ,,,,,,,,,, - 1 , 6 , 13 ,,,,,,,, 496

so we get 143 terms , so our answer is 143