There are no solutions because the discriminant of this quadratic equation is less than zero
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The person or program that solves the equation does.
The equation has infinitely many solutions.
The equation has no solution. Since if you combine like terms, you get 0=-10 which isn't true, there are no solutions to the equation.
There are a number of possible solutions which will have x=2 and y = 10 as solutions but many of them will also allow other solutions. One possibility, with a unique solution, is (x-2)2 + (y-10)2 = 0
Using the quadratic equation formula: x = 1 or x = -10