Solve the following system of equations

8v-3u=5uv

6v-5u=-2uv

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Solution

Divide both sides by uv:
8/u-3/v=5,6/u-5/v= -2
Take 1/u=x and 1/v=y,so the eqn becomes
8x-3y=5.. (i)and 6x-5y= -2.. (ii) then multiplying (i) by 5 and (ii) by 3 we get 40x-15y=25..(iii) and 18x-15y= -6.. (iv) then subtract iv from iii,
12x=31 i. e. X=31/12,
Put x=31/12 in (i) to get
62/3 -3y=5 solve
Y=47/9 then
U=1/x so u=12/31,
V=1/y so v=9/47

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