Here is a system of linear equations:
$$x_1+x_2=20$$ $$x_2+x_3=20$$ $$-x_1+x_5=10$$ $$x_3-x_4=-20$$ $$x_4-x_5=10$$
I managed to express each variable in terms of $x_1$. $$x_1=x_1$$ $$x_2=-x_1+20$$ $$x_3=x_1$$ $$x_4=x_1+20$$ $$x_5=x_1+10$$
But I can't seem to find the value of any one variable.
I did try choosing random values for $x_1$ and finding the other values from that. I tested it for $x_1=0$ and $x_1=10$. The 2 sets obtained satisfied the system of equations. It seems that there are multiple or infinite solutions to this system.
But I have 5 equations with 5 unknowns. Shouldn't I be able to solve that? How do I show/prove the number of solutions to this system of equations?