Why do you square both sides when it's the square root of x^2+y^2=4? why don't you just take the square root of each side, making it 2=x+y?

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Also, think of this example. 3^2 + 4^2 = 5^2   (9 + 16 = 25) not true that 3 + 4 = 5

you have to try to get the answer into the standard form of a circle. By taking the square root of both sides, you make it a line, not a circle.