Precalc help?

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1 Answer
George C.
May 28, 2018

(x, y, z) = (1, -1, 2)

Explanation:

Given:

{ (2/x-1/y+2/z=4), (1/x+2/y-2/z=-2), (3/x+3/y+4/z=2) :}

Note that if we define X=1/x, Y=1/y and Z=1/z, then we get linear equations:

{ (2X-Y+2Z=4), (X+2Y-2Z=-2), (3X+3Y+4Z=2) :}

We can eliminate Z from the first equation by adding the second equation to it. We can eliminate Z from the third equation by adding twice the second equation to it. These two combinations give us:

{ (3X+Y=2), (5X+7Y=-2) :}

To eliminate Y, we can subtract 7 times the first equation from the second to get:

-16X=-16

Hence X=1.

Then substituting this value of X in 3X+Y=2 we find Y=-1.

Then substituting the values X=1 and Y=-1 in 2X-Y+2Z=4, we find Z=1/2

Hence x=1/X=1, y = 1/Y=-1 and z=1/Z=2

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