HP 50g / HP Prime: Solve equation with 3 variables

[rawi]

There are two ways:
1st: In essence you have a system of linear equations that can be written as follows:
1*A+1*B+0*C=5; 0*A+1*B+2*C=-3; 3*A+0*B+1*C = 10.
This can be solved by
Press Shift NUM.SLV, press 4 for Solve linear equation, press enter.
You get a mask. Put in A by [[1,1,0],[0,1,2],[3,0,1]] presse Enter
Put in B by [5,-3,10] press enter
Press Solve (right softkey)
You get the answer in the line with x: [4,1,2]
2nd: The more general ways for all kinds of systems of equations, not just linear:
Set to ALG mode (perhaps works as well in RPN mode)
Press shift NUM.SLV, press 6 for MSLV
MSLV() is shown
Put in the brackets three vectors: One with in equations, one with paramters for which to solve, one with initial guesses.
Here it looks like this:
MSLV([A+B-5=0, B+2*C+3=0,C+3*A-10=0],[A,B,C],[0,0,0])
Then an iterative process starts. After a few seconds you get the same result.
Hope this helps a bit.