Find the solution to the non-homogeneous linear system below. $$\begin{aligned}-x_1 - x_2 + x_3 + x_4 + x_5 &= 2\\-x_1 - x_2 + 2x_3 - x_5 &= 4\\-x_1 - x_2 + 2x_3 &= 5\\-x_1 - x_2 + 2x_4 + 4x_5 &= 1\end{aligned}$$
Write your solution using parameters $s$, $t$, etc. For example
$\text{sol}=x_\text{part}+\text{sol}_\text{hom}={(1,2,3,4,5)+s(1,0,0,0,0)+t(0,1,0,0,0)}$
So, I have this question to solve but, it takes so much time for me to solve these kinds of problems is there any way to solve it much faster, if there is can you show me please.