Hi Ashish :)
You can easily check that there is some problem in the answer you have posted.
As per your answer, the equilibrium allocation for consumer 1 is (x_1*, y_1*) = (1,0) and equilibrium prices (px, py) = (1,1/4) .
At the above price ratio, income of consumer 1 = 0*1 + 1*1/4 = 1/4
But the allocation (x_1*, y_1*) = (1,0) is not affordable.
I think you have done some calculation error while finding equilibrium allocation.
:)