Consider the following system of equations:

$$e\_1^1+e\_1^2K=e\_1^3J+e\_1^4G\tag{1}$$

$$e\_2^1J+e\_2^2G=e\_2^3T\tag{2}$$

$$e\_3^1+e\_3^2K=e\_3^3J+e\_3^4G\tag{3}$$

$$e\_4^1J+e\_4^2G=e\_4^3T\tag{4}$$

where $e\_n^m$ , $n,m=1,2,3,4$ are constants. I tried many times to solve it for $T$ by myself but I couldn't. I also looked for software to get a general solution for such system of equations but I didn't find any. I tried with equations (3) and (4) and I just got the following equations;

$$J=\frac{e\_4^3 e\_2^2-e\_4^2 e\_2^3}{e\_4^1 e\_2^2-e\_4^2 e\_2^1}T$$

$$G=\frac{e\_4^3 e\_2^1-e\_4^1 e\_2^3}{e\_4^2 e\_2^1-e\_4^1 e\_2^2}T$$

I don't know how I should continue to get the general solution for $T$ in term of $e\_n^m$. Can anyone here help me out please?