tricky algebra problem

[opaque ivy]

I want to be able to solve this in a more systematic way

because I can easily turn this into x^2 - y^2 = 40

wherein I can infer that x is 7 and y is 4

but I don't want that

I want to be able to solve this systematically

[pallid trout]

so

basically

if we divde first equation with x, is x+y= 28/x

amd if we devide seond one by y, it is y+x=-12/y

so find how many piars match 28/x=12/y

[north wadi]

I would say that
28 – 12 = x² + 2xy + y²
14 = (x + y)²
x + y = √14

So
28/x = √14 – 12/y = √14
x = 28/√14 y = – 12/√14

[north wadi]

The problem is solved

[opaque ivy]

.solved