Question

Solve the following system of equations:

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

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

Answer 1

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

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`

Substituting `1/(x - 1)` for 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 equations.