Hi Karthik,
Using the Wolfram Language your system of equations has to be written as follows:
Solve[{o a + n b + m c == r x, n d + m e == (r + o) c,
o d + m f == (r + n) b, m g == (r + n + o) d,
r x + o e + n f == (m + r) a, r c + n g == (m + o + r) e,
r b + r a + o g == (m + n + r) f,
r d + r e + r f == (m + n + o) g}, {x, a, b, c, d, e, f, g}]
And the solution is:
{{x -> 0, a -> 0, b -> 0, c -> 0, d -> 0, e -> 0, f -> 0, g -> 0}}
Note: The input is too long for Wolfram|Alpha. So, I used Mathematica. Probably you could also use the Wolfram|Alpha Pro.