X2+y2=61 x2-y2=11 решите

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To solve this system of equations, we can add the two equations together to eliminate the y^2 terms:

X^2 + y^2 + x^2 - y^2 = 61 + 11
2x^2 = 72
x^2 = 36
x = 6 or x = -6

Now we can substitute the value of x back into one of the equations to solve for y:

For x = 6:
6^2 + y^2 = 61
36 + y^2 = 61
y^2 = 25
y = 5 or y = -5

So the solutions to the system of equations are:
x = 6, y = 5
x = 6, y = -5
x = -6, y = 5
x = -6, y = -5