JEE Main202125 Feb 2021Evening ShiftMathematicsDeterminantsActual

The following system of linear equations 2 x + 3 y + 2 z = 9 3 x + 2 y + 2 z = 9 x - y + 4 z = 8

Options

Ahas infinitely many solutions
Bhas a unique solution
Chas a solution α , β , γ satisfying α + β 2 + γ 3 = 12
Ddoes not have any solution

Correct answer

B. has a unique solution

Step-by-step solution

2 x + 3 y + 2 z = 9       . . . 1 3 x + 2 y + 2   z = 9     . . . 2 x - y + 4 z = 8       . . . 3 1 - 2 ⇒ - x + y = 0 ⇒ x - y = 0 from 3   4 z = 8 ⇒ z = 2 from 1   2 x + 3 y = 5 ⇒ x = y = 1 ∴ system has unique solution.

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