Solve for x and y

We have

and

where x≠0 and y≠0

Lets simplify these equations. Assuming 1/x = p and 1/y = q, we can rewrite them,

⇒ 3p – q = - 9 …(i)

⇒ 2p + 3q = 5 …(ii)

To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.

Lets multiply eq.(i) by 3, so that variable q in both the equations have same coefficient.

Recalling equations (i) & (ii),

3p – q = - 9 [×3

2p + 3q = 5

⇒ 11p = - 22

⇒ p = - 2

Substitute p = - 2 in eq.(i)/eq.(ii), as per convenience of solving.

Thus, substituting in eq.(i), we get

3( - 2) – q = - 9

⇒ - 6 – q = - 9

⇒ q = 9 – 6

⇒ q = 3

Thus, p = - 2 and q = 3

As p = 1/x,

⇒ - 2 = 1/x

⇒ x = - 1/2

And q = 1/y

⇒ 3 = 1/y

⇒ y = 1/3

Hence, we have x = - 1/2 and y = 1/3