Solution to Ramanujan equations

Solution to Ramanujan equations $\sqrt{(}x)+y=7$$\sqrt(x) + y = 7$ and $x+\sqrt{(}y)=11$$x + \sqrt(y) = 11$ with Python

Observation : both $x$$x$ and $y$$y$ are perfect squares below 121(11*11).

​x
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import math
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sq = [x*x for x in range(1,12)]
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for x in sq:
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    for y in sq:
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        if math.sqrt(x) + y == 7 and x + math.sqrt(y) == 11:
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            print(x,",",y)
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#9,4
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#https://ideone.com/2XMNUh

It can be seen that $x=9$$x = 9$ and $y=4$$y = 4$ are the solutions.