-5x+4y=19
This is called a Linear Diophantine equation and has an infinite number of solutions, such as:
x=1, y=6 or x=5, y=11 or x=9, y=16.........etc.
+118667 It is not a diophantine equation. Or at least there is no reason to think that it is.
It is just the equation of a line, passing through(0,19/4) and (-19/5,0), and yes there are infinite solutions.
ax + by = 1 This is a linear Diophantine equation. x , y are the unknowns, a, b are given constants.
https://en.wikipedia.org/wiki/Diophantine_equation
Look under "Examples"
A Diophantine equation is an equation in which only integer solutions are allowed.
http://mathworld.wolfram.com/DiophantineEquation.html
