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The system of equations \[ x+4y+6z=20,\qquad x+y+z=6,\qquad x+\lambda y+6z=20 \] has

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Whenever a parameter appears in a system of linear equations, reduce the augmented matrix first. Then examine the special value(s) of the parameter separately to check whether the system is consistent, inconsistent, or has infinitely many solutions.

Updated On: Jul 23, 2026

Solution for any value of \(\lambda\)
No solution for \(\lambda=4\)
Unique solution for \(\lambda=4\)
Infinite solutions for \(\lambda\neq4\)

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The Correct Option is A

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The system of equations \[ x+4y+6z=20,\qquad x+y+z=6,\qquad x+\lambda y+6z=20 \] has

Show Hint

The Correct Option is A

Solution and Explanation

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