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If the following system of linear equations 2x + y + z = 5 x − y + z = 3 x + y + az = b has no solution, then :

1. a = −1/3, b ≠ 7/3
2. a ≠ 1/3, b = 7/3
3. a ≠ −1/3, b = 7/3
4. a = 1/3, b ≠ 7/3

Correct answer: a = 1/3, b ≠ 7/3

Solution

The system has no solution when the equations are inconsistent, which occurs when the third equation does not align with the first two. Setting a to 1/3 ensures that the third equation is dependent on the first two, while b must be different from 7/3 to prevent the equations from intersecting.

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