I took a test in math to determine where I was etc etc... anyways, the following question came up: How many answers are there to the following system of equations? x^2 + 5y = 30 x^2 + (y-3)^2 = 9 a) 0 b) 1 c) 2 (my answer) d) 3 (correct answer) The first thing I noticed was that x was the same thing in both cases, the answer would not be changed because of it. As such, x could be almost any value (infinite answers). So obviously, they wanted how many solutions for Y. My work (in my head) was: x^2 + 5y = 30 x^2 + (y-3)^2 = 9 *subtract equations from each other 5y - (y-3)^2 = 21 *break (y-3)^2 5y - (y^2 - 6y + 9) = 21 5y - y^2 + 6y - 9 = 21 11y - y^2 = 30 *place ^2 in positive and use ax^2 + bx + c format y^2 - 11y + 30 = 0 *check for 2 or 1 answers by checking if the sqr() portion of quadratic formula is non zero sqr(121 - 4*30*1) = sqr(1) = 1 since 1 <> 0, and the answer will be +- 1, there are two answers. Where is my mistake?