Lol, that's a fallacy
From the equation, we are subject to determine the values of the variables, x and y. Isn't it?
Not the values of the constants.
Taking your calculations, we get
Multiply both sides by x:
Subtract y^2 from both sides:
Factorise both sides:
Divide both sides by (x-y):
putting the value of x in the initial condition, we get
To determine any other values of x and y, we need at least one more equation.
Number of possible outcomes are calculated as "number of possible outcomes in a trial to the power number of trials".
Number of possible outcomes for tossing a coin thrice (as good as John's original question) =8 (2*2*2). For throwing a die thrice= 216 (6*6*6). For drawing a card 3 times (with replacement) from a pack = 140608 (52*52*52).