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8v-3u=5uv. 6v-5u=-2uv Related: Maths Intro to Euclid ...
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 eq. 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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