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Solve the system to find (u,v): 3/u + 4/v = 1 6/u - 2/v = 1I don't understand thiis =(

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jfk4got2duck | Student, Grade 11 | eNotes Newbie

Posted August 5, 2011 at 11:17 AM via web

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Solve the system to find (u,v):

3/u + 4/v = 1

6/u - 2/v = 1

I don't understand thiis =(

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beckden | High School Teacher | (Level 1) Educator

Posted August 5, 2011 at 12:49 PM (Answer #1)

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(1) `3/u + 4/v = 1`
(2) `6/u - 2/v = 1`

Solve (1) for v
3v + 4u = uv   Multiply by uv.
4u = uv - 3v
4u = v(u - 3)
(3) `v = 4u/(u - 3)`

Substitute this into (2)
`6/u - 2/(4u/(u - 3)) = 1`
`6/u - 2(u-3)/(4u) = 1`
`12/(2u) - (u-3)/(2u) = 1`
`(12 - (u - 3)) / 2u = 1`
12 - u + 3 = 2u
15 = 3u
u = 5

Substitute into (1)
`3/u + 4/v = 1`
`3/5 + 4/v = 1`

`4/v = 2/5`
`4/v = 2/5`

 

`v = 4*5/2 = 10 `

Check
(1) `3/5 + 4/10 =^? 1`` `

`6/5 + 4/10 = 1 ` Check
(2) `6/5 - 2/10 ?= 1`
`6/5 - 1/5 = 1` Check

So the answer is u = 5, v = 10.

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