Solve for x and y:

 (CBSE 20007)

We have

and

Lets simplify these equations. Assuming 1/y = z, we can rewrite them,

⇒ x + 6z = 6 …(i)

⇒ 3x – 8z = 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 “x” in both the equations have same coefficient.

Recalling equations (i) & (ii),

x + 6z = 6 [×3

3x – 8z = 5

⇒ 26z = 13

⇒ z = 13/26

⇒ z = 1/2

Substitute z = 1/2 in eq.(i)/eq.(ii), as per convenience of solving.

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

x + 6(1/2) = 6

⇒ x + 3 = 6

⇒ x = 3

Thus, z = 1/2 and x = 3

As z = 1/y,

⇒

⇒ y = 2

Hence, we have x = 3 and y = 2