$$|3x-2y-11|+2\sqrt{31-8x+5y}=0$$
I was confused at first as there are clearly 2 vars but only 1 equation, but the textbook does have an answer.
What I tried:
Setting some bound by letting the ordered tuple (x,y) be a solution and then by assuming x < y create some sort of inequality. That got me nowhere.
I then tried to do this "properly" and move the sqrt business to the RHS, square everything, simplify and end up with an ugly multi-var polynomial = 0. I could not factorise it neatly. I was sure this had to work but wolfram alpha agreea with me as well. I got stuck again.
Please need a a new idea, approach or hint. Thanks.