The code is like this:
syms x y z
eqns = [x + y == 1, x + z == 2, z - y == 0.5];
vars = [x y z];
[solx, soly, solz] = solve(eqns,vars)
But the result is like this:
solx =
Empty sym: 0-by-1
soly =
Empty sym: 0-by-1
solz =
Empty sym: 0-by-1
Why is this not working?
Let's recast your problem as a numerical linear algebra problem:
A = [1 1 0; 1 0 1; 0 -1 1];
b = [1; 2; 0.5];
result = A\b
result =
1.00000
0.16667
0.83333
Aside from the result, you get a warning:
warning: matrix singular to machine precision
That should tell you the answer: your system is not solvable. You can determine the same thing manually by subtracting the first equation from the second:
x + z == 2
- x + y == 1
-------------
z - y == 1
This contradicts z - y == 0.5, so your system does not have a valid solution.