SOLUTION: Using Cramer’s rule method, find the value of x and y when given the following two equations, x+y+1/x+y-1 = 2 and x+y-1/x-y-1 = -1

Algebra ->  Matrices-and-determiminant -> SOLUTION: Using Cramer’s rule method, find the value of x and y when given the following two equations, x+y+1/x+y-1 = 2 and x+y-1/x-y-1 = -1       Log On


   

Question 1147384: Using Cramer’s rule method, find the value of x and y when given the following two equations, x+y+1/x+y-1 = 2 and x+y-1/x-y-1 = -1
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.

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


    %28x%2By%2B1%29%2F%28x%2By-1%29 = 2      (1)

    %28x%2By-1%29%2F%28x-y-1%29 = -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.