Question

Solve the following pair of equations :
[5/(x–1)] + [1/(y– 2)] = 2 , [6/(x–1)] – [3/(y–2)] = 1

Answer 1

The answer is x=4 and y =5.

Answer 2

x = 4 and y = 5

Explanation:

Given: [5/(x–1)] + [1/(y– 2)] = 2 , [6/(x–1)] – [3/(y–2)] = 1

Let 1/(x-1) = u and 1/(y-2) = v

Then we get equations as:

5u + v = 2 -------(1)

6u - 3v = 1 ------(2)

(1) * 3 ==> 15u + 3v = 6

(2)       ==> 6u    - 3v = 1

Adding==> 21u = 7

u = 7/21 = 1/3

Substuting u in equation 2, we get:

6 (1/3) - 3v = 1

-3v = 1-2

v = -1/-3 = 1/3

1/x-1 = 1/3, so x-1 = 3, x = 4.

1/y-2 = 1/3, so y-2 = 3, y = 5.