As you can see and have the same variables, solve it simultaneously and take only real numbers as your solution. To prove that the points are vertices of a square,
i) Multiply the gradient of both the diagonals and show that it is -1.
ii)Find the distance of the diagonals, they should be equal
Sorry. but your solution above makes no sense. Anyway here is my solution;
let
be equation (1)
be equation (2)
multiply (1) by 9;
--------(1a)
multiply (2) by 4;
---------(2a)
(1a)-(2a);
substitute and into one of the original equations, in this case (1)
therefore you have
as the solution/coordinates of vertices
and as you can see, they are all equidistant from the origin and that by itself shows that a quadrilateral formed by joining the points would be a square