Solve for one of the variables first. X will do here for the first one.
5X - 4Y = 3
5X = 4Y + 3
X = (4/5)Y + 3/5
------Substitute back into original equation.
5(4/5Y + 3/5) - 4Y = 3
4Y + 3 - 4Y = 3
Y = 0 (obviously)
------Insert back into original equation.
5X - 4(0) = 3
5X = 3
X = 3/5
======Check.
5(3/5) - 4(0) = 3
15/5 = 3
3 = 3
======Checks.