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The system of equations $2x + y = 2z$, $y + z = 0$, $3y + \alpha z = x$ has:

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When options give a specific parametric solution form like $(3k, -2k, 2k)$, directly plug it back into the easiest equations to verify if it satisfies them identically. This saves the time needed to compute complex determinants.

Updated On: Jul 9, 2026

No solution for any value of $\alpha$
Infinite number of solutions for $\alpha = \frac{7}{2}$
Only trivial solution for $\alpha = \frac{9}{2}$
Infinite solutions of the form $(3k, -2k, 2k)$

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The Correct Option is D

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Show Hint

The Correct Option is D

Solution and Explanation

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