Looking on the form the equations are written and presented, I only can guess that the equations are


     = 2      (1)

     = -1     (2)


Then from equation (1) you have


    x + y + 1 = 2*(x+ y - 1),

    x + y + 1 = 2x + 2y - 2

    1 + 2 = x + y

    x + y = 3


From equation (2)

   
    x + y - 1 = -(x - y - 1)

    x + y - 1 = -x + y + 1

    2x = 2.


Thus the given system of nonlinear equations is equivalent to this system of linear equations


    x + y = 3,      (3)

    2x    = 2.      (4)


The solution of the system (3),(4) is VERY SIMPLE :  x = 1,  y = 2.


It does not require using the Cramer's method.