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Consider the following system of equations: $x + 2y - 3z = a$, $2x + 6y - 11z = b$, $x - 2y + 7z = c$
where $a, b$ and $c$ are real constants. Then the system of equations:
(1) has a unique solution when $5a = 2b + c$
(2) has infinite number of solutions when $5a = 2b + c$
(3) has no solution for all $a, b$ and $c$
(4) has a unique solution for all $a, b$ and $c$
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