Today I have a question and I am really curious to know about this.
Question:
$$ 16y+39z+50zy=0$$
$$ 85x-78z+95zx=0$$
$$ 85x+32y+70xy=0$$
$$\text{Are The Equations like these can be solve for unknowns? If not Why?If so How?}$$
I derived those from these:
$$ 1/x+1/y-1/z=-1$$
$$ 4/x+3/y+2/z=16$$
$$ 2/x-2/y-3/z=5$$
Best Answer
If you derived the system of the equations correctly, you then get a normal 3x3 system equation with first-degree set of variables. This is a common linear algebra problem and can be solved in a ton of ways.
First of all, express $\frac{1}{x} = i , \frac{1}{y} = j , \frac{1}{z} = k$
Then you will have the following :
$ i + j + k = 1, 4i + 3j + 2k = 16, 2i - 2j - 3k = 5 $
In order to show that these can be solved or not, you can apply the Gauss Method on the matrix of their coefficients. Be careful after that, on probable solutions that may not apply for the starting fractions ($\frac{1}{x}$etc )