$\displaystyle x-y+3z=1,
2x+z=0,
-x+y-3z=0$
Please let me know how to solve this question
I am not sure what the title of this thread has to do with the problem, but...
To solve this you will want to solve for $\displaystyle x$ in the first equation, then substitute that into the second equation. Now solve for $\displaystyle y$ in the second equation, then substitute that and what you got for $\displaystyle x$ into the third equation. At this point the third equation should be in terms of $\displaystyle z$ only. Finally, sovle for $\displaystyle z$. This last step will give you a number. Now use this to determine $\displaystyle y$ and finally use both $\displaystyle y,z$ to determine $\displaystyle x$.