Question

Solve the following systems of equations:

`2(1/x) + 3(1/y) = 13`

`5(1/x) - 4(1/y) = -2`

 

Answer 1

Let us write the given pair of equation as

`2(1/x) + 3(1/y) = 13`  ....(1)

`5(1/x) - 4(1/y) = -2` ....(2)

These equation are not in the form ax + by + c = 0 However, if we substitute

`1/x = p` and `1/y = q` in equation (1) and (2) we get

2p + 3q = 13

5p - 4q = -2

So, we have expressed the equations as a pair of linear equations. Now, you can use any method to solve these equations, and get p = 2, q = 3

You know that `p =1/x and q =1/y`

Substitute the values of p and q to get

`1/x = 2 i.e x = 1/2 and 1/y = 3 " i.e " y = 1/3`