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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

Correct answer: has infinite number of solutions when 5a = 2b + c

Solution

The condition 5a = 2b + c indicates that the equations are dependent, meaning they represent the same geometric plane in three-dimensional space, which results in infinitely many solutions.

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