(x - 2)/5 +y/2 = 6.............(1)

(x - 1)^2 -(y - 2)^2 = (x - y)(x + y) - 59...........(2)

First let us re-write both equations:

(x-2)/5 + y/2 = 6

Let us multiply by 10:

==> 2(x-2) + 5y = 60

==> 2x + 5y = 64 ........(3)

Now for equation (2):

(x-1)^2 - (y-2)^2 = (x-y)(x+y) - 59

==> x^2 - 2x + 1 - y^2 + 4y - 4 = x^2 - y^2 - 59

==> -2x + 4y - 3 = -59

==> -2x + 4y = -56 .........(4)

Now let us add (3) and (4):

==> 9y = 8

==> y = 8/9

Now to calculate x, we will substitute in (4):

2x = 4y + 56

==> x = 2y + 28

==> x= 2*8/9  + 28 = 16/9 + 28 = 268/9

==> x= 268/9