It has many solutions, an infinite number, but the equation can be simplified to x+y=2 by dividing both sides by 2. All the equation does is relate the values of x and y, so if you know x you can find y, and vice versa. You can draw a straight line graph and every point on the line represents a solution, but the line goes on forever.
Examples:
If x=0, y=2 and if y=0, x=2 are two examples and there are many others (x=1 and y=1), etc.)