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For the system x + y + a z = b, 2x + 3y = 2a, 3x + 4y + a² z = ab + 2, which statement is correct?

1. it has infinitely many solutions when a = 1, for every real b
2. it has a unique solution when a is not 0 and b is any real number
3. it has no solution when a = 0, b = 1
4. it has infinitely many solutions when a = 0, b = 2

Correct answer: it has infinitely many solutions when a = 1, for every real b

Solution

When a = 1 the determinant is zero and equation 3 equals equation 1 plus equation 2 for every b, so the system is consistent with infinitely many solutions for all real b.

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