# 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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### 1 Answer

(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.