Solution : By inspection, x=2,y=2 is a solution because for x=2,y=2
x+2y=2+4=6
Now, let us choose x=0. With this value of x, the given equation reduces to 2y=6 which has the unique solution y=3. So x=0,y=3 is also a solution of x+2y=6. Similarly, taking y=0, the given equation reduces to x=6. So, x=6,y=0 is a solution of x+2y=6 as well. Finally, let us take y=1. The given equation now reduces to x+2=6, whose solution is given by x=4. Therefore, (4,1) is also a solution of the given equation. So four of the infinitely many solutions of the given equation are:
(2,2),(0,3),(6,0) and (4,1)