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Question

x+y=5xy,3x+2y=13xy.

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Solution

The given equations are:
x + y = 5xy .......(i)
3x + 2y = 13xy .........(ii)

From equation (i), we have:

x+yxy=5
1y+1x=5
.............(iii)

From equation (ii), we have:

3x+2yxy=13
3y+2x=13
.............(iv)
On substituting 1y=v and 1x=u , we get:
v + u = 5 ...........(v)
3v + 2u = 13 ...........(vi)

On multiplying (v) by 2, we get:
2v + 2u = 10 ..............(vii)
On subtracting (vii) from (vi), we get:
v = 3
1y=3y=13
On substituting y=13 in (iii), we get:
113+1x=5
3+1x=51x=2x=12
Hence, the required solution is x=12 and y=13 or x = 0 and y = 0.

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