$ \frac{a_1}{x} + \frac{b_1}{y} + \frac{c_1}{z} = d_1 \\ \frac{a_2}{x} + \frac{b_2}{y} + \frac{c_2}{z} = d_2 \\ \frac{a_3}{x} + \frac{b_3}{y} + \frac{c_3}{z} = d_3 $
$ a_i, b_i, c_i, d_i $: known constants
$ x, y, z $: unknown variables
First of all, is this equation set linear?
I want to learn method(s) of solving this kind of equation sets by using paper and pencil only. The point in which I'm stuck is that, when I equate the denominators, the equation turns into a non-linear form like below:
$ a_1yz + b_1xz + c_1xy = d_1xyz \\ a_2yz + b_2xz + c_2xy = d_2xyz \\ a_3yz + b_3xz + c_3xy = d_3xyz \\ $
What is the proper way(s) of solving this equation set?