Yes, it is the only solution.
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If you mean to say (x^2)-2x+4=0 then there is no solution for x because the equation never makes it to 0 If you mean to say 2x-2x+4=0 then there is no solution for x because it is a horizontal line at Y=4
If you have -2x = 0, to solve for x, divide each side by two. That results in x = -0/2, or x = 0. So there is only one solution.
y = 0x = y + 2plug 0 in for yx = 0 + 2x = 2
1 +/- the square root of 3
x = 0 & y = -3