- #1

Appleton

- 91

- 0

## Homework Statement

Find three numbers x,y,z satisfying the following equations:

9x-6y-10z=1

-6x+4y+7z=0

x

^{2}+y

^{2}+z

^{2}=9

## Homework Equations

## The Attempt at a Solution

The book suggests that the best approach is to express 2 unknowns in terms of the third unknown from the first 2 linear equations and, by substituting these expressions in the last equation, obtain a quadratic equation for the third unknown.

So i try this:

4(9x-6y-10z=1)= 36x-24y-40z=4

6(-6x+4y+7z=0)= -36x+24y+42z=0

(36x-24y-40z=4) + (-36x+24y+42z=0)= 2z=4

z=2

I figure I've gone wrong somewhere because this is not the strategy outlined in the book (it's also not the correct answer for z according to the book)