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Question

Solve for x and y:

3x+y+2xy=2,9x+y4xy=1.

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Solution

3x+y+2xy=2,9x+y4xy=1

Let 1x+y=u

Let 1xy=v

Soln:

Then the given system of the equation becomes:

3u+2v=2…….. (i)

9u4v=1……....(ii)

Multiplying equation (i) by 2 and (ii) by 1

6u+4v=4…………… (iii)

9u4v=1…………..... (iv)

Adding equation (iii) and (iv) we get,

15u=5

u=13

multiplying equation (i) by 3

9u+6v=6.......(v)

Subtracting equation (iv) from equation (v) , we get

2v=21

2v=1

v=12

Now,

1x+y=u=13

=x+y=3……………..(vi )

1xy=v=12

=xy=2…………………..(vii)

Adding equation (vi) and (vii) we get,

2x=5

=x=52

Putting the value of x in equation (vi)

52+y=3

y=12

The solutions of the given system of equation are 52 and 12 respectively.


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