There is a linear system of 4 equations in field $Z_p$ with 4 unknowns $k_1$, $k_2$, $x_1$, $x_2$. The other variables s, r and h are known.
Please show me all the steps using Gaussian Elimination or any other method to get from the four modular linear equations below to solve for X. I know the answer for X but I want to be shown so I can understand all the steps how you can use Gaussian Elimination or any other method to get to the answer for $x_1$.
These are the four modular linear equations:
$s_1k_1 - r_1x_1 = h_1$ (mod p)
$s_2k_1 - r_1x_2 = h_2$ (mod p)
$s_3k_2 - r_2x_1 = h_3$ (mod p)
$s_4k_2 - r_2x_2 = h_4$ (mod p)
(in the equations above h is congruent)
to:
$x_1 = \frac{(h_1r_2s_2s_3 - h_2r_2s_1s_3 -h_3r_1s_1s_4 + h_4r_1s_1s_3)}{r_1r_2(s_1s_4 - s_2s_3)}$
where operations including division are in the multiplicative group $Z_p$.
So to clarify I would like you to show me how to use Gaussian Elimination or any other method and all the steps involved to get to the above given answer for x1 please.