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Question

Solve the following pair of equations.

7x2yxy=5

8x+6yxy=15

Here, x 0 and y 0.


A

x = 2, y = -5

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B

x=52, y is not defined

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C

x=25, y is not defined

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D

x=43, y=72

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Solution

The correct option is C

x=25, y is not defined


7x2yxy=5

7xxy2yxy=5

7y2x=5

Similarly we can do the same for the second equation.

8x+6yxy=15

8y6x=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.


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