False.

3(1) + 4(1) = 7
      3 + 4 = 7
          7 = 7
So (x,y) = (1,1) is one solution.


3(-7) + 4(7) = 7
    -21 + 28 = 7
           7 = 7
So (x,y) = (-7,7) is another solution.


3(-3) + 4(4) = 7
     -9 + 16 = 7
           7 = 7
So (x,y) = (-3,4) is another solution.


3(5) + 4(-2) = 7
      15 - 8 = 7
           7 = 7
So (x,y) = (5,-2) is another solution.



       2 + 5 = 7
           7 = 7
So (x,y) =  is another solution.



There are an infinite number of solutions.

Edwin