Question

Solve u and v.
2(3u-v)=5uv
2(u+3v)=5uv

Answer 1

2(3u - v) =5uv

6u - 2v =5uv ……(1)


2(u+3v)=5uv

2u + 6 v =5uv …[2]

(2) ✖ 3 = 6 u + 18 v =15 uv …(3)


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(3)-(1)

6 u + 18 v =15 uv

6u - 2v =5uv
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20 v = 10 uv


20=10u

u =2

substitute 2(u+3v)=5uv

2( 2+3v) =5(2) v

4+6v =10v

4=4v


v = 1


Therefore, ( u, v) =(2,1)

Answer 2

Answer:2(3u-v) = 5uv

dividing by uv

⇒(6/v)-(2/u) = 5

Let 1/v = x and 1/u =y

⇒6x -2y =5

⇒18x -6y =15____(1)

similarly, (2/v)+(6/v)=5

⇒2x +6y =5____(2)

adding (1) and (2), we get

20x =20

⇒x=1

so, y =(5-2)/6 = 1/2

x=1 so 1/v =1

⇒v =1

and y=1/2 = 1/u

⇒u=2 

Step-by-step explanation: