Question

Solve the following systems of equations:

`5/(x - 1) + 1/(y - 2)  = 2`

Answer 1

Let us put` 1/(x  - 1) = p and 1/(y - 2) = q` The the given equation

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

`6(1/(x - 1))  -3 (1/(y - 2) ) = 1` ....(2)

Can be written as 

5p + q = 2 ....(3)

6p - 3q = 1 ...(4)

Equation 3 and 4 from a pair of linear equations in the genera; form. Now you can use any method to solve these equation we get p = 1/3 and q = 1/3 now

substituting `1/(x - 1)` fpr p we have

`1(x - 1) = 1/3`

i.e x - 1 = 3 i.e x = 4

Similary substituting 1/(y -2) for q we get

`1/(y -2) = 1/3`

i.e 3 = y - 2 i.e y = 5

Hence x = 4, y = 5 is required solution of the given pair of euation