Solve the system. Hint: let u = 1/x, v=1/y, and w=1/z, and solve the resulting system.)

3/x + 4/y - 1/z = 38

1/x + 2/y - 1/z = 20

2/x + 2/y - 3/z = 39

The solution of the system are x = , y = , and z = .

Convert the system in u, v and z as suggested.

So 3u +4v-w = 38. ---- (1)

u +2v-w = 20 ----- (20

2u + 2v -3w. = 39 -----(3)

Subtract (2) from (1) and you get 2u+ 2v = 18

Plug in 2u+2v= 18 in (3). So w= -7

Now (1) is. 3u+4v +7 =38 so. 3u +3v =31. ----------(4)

But we have u+v =9 which is = 3u+3v = 27. -------(5)

Solve (4) and (5) and you get v =4

Plug v = 4 in (4) and you get u=5

Now you have u=1/x = 5. So x= 1/5

v = 1/y = 4. So y = 1/4.

w= 1/z = -7. So z = -1/7

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