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Question

Solve:
8u - 3v = 5uv
6u - 5v = -2uv

A
u=1323,v=2233
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B
u=115,v=1322
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C
u=1123,v=2231
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D
Insufficient data
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E
None of the above
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Solution

The correct option is C u=1123,v=2231
8u - 3v = 5uv,
6u - 5v = -2uv
Dividing both equations by uv, we get
8v3u=5 and 6v5u=2,
Putting, 1v=x and 1u=y, we get
8x3y=5(1)
and 6x5y=2(2)
Multiplying Equation (1) and Equation (2) by 6 and 8, respectively, we have,
48x18y=30 and 48x40y=16
Subtracting the second equation from the first, we get
22y=46, i.e., y=2311
From Equation (1), x=(5+3y8)=(5+3(2311))8=3122
u=1y=1123 and v=1x=2231

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