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Question

Solve the following system of equations:
8v3u=5uv
6v5u=2uv

A
u=3122, v= 2311
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B
u=3122, v= 1123
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C
u=2231,v=1123
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D
u=2231,v=2311
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Solution

The correct option is C u=2231,v=1123
Divide the given equations by uv,
8v3u=5uv8u3v=5...(1)
6v5u=2uv6u5v=2...(2)

Assume 1u=x and 1v=y
Put the values of 1u and 1v in (1) and (2)
8x3y=5...(3)
6x5y=2...(4)

Solving equations (3) and (4) we get x and y
Multiply (3) with 5 and (4) with 3 to equate the coefficients of y.
40x15y=25
18x15y=6

x=3122u=2231

Substituting x in (3)
8×31223y=53y=6911

y=2311v=1123

So, u=2231 and v=1123

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