Solve the following pair of equations.
7x−2yxy=5
8x+6yxy=15
Here, x ≠ 0 and y ≠ 0.
x=−25, y is not defined
7x−2yxy=5
⇒7xxy−2yxy=5
⇒7y−2x=5
Similarly we can do the same for the second equation.
8x+6yxy=15
⇒8y−6x=15
Now we can see that the equation is not linear. So we will assume 1x=u and 1y=v
So, the pair of equation can be written as
-2u + 7v = 5
-6u + 8v = 15
We can solve the pair of equation by method of elimination.
On multiplying equation -2u + 7v = 5 by 3 we get
-6u + 21v = 15 ...(1)
-6u + 8v = 15 ...(2) (given)
On subtracting equation (2) from equation (1), we get 13v = 0 i.e. v = 0
On substituing v = 0 in equation -2u + 7v = 5, we get
u=−52
We know that 1x=u and 1y=v
∴x=−25
and y=10, which is not defined.