Q46 / 90 · JEE Main 2021 (25 Feb Shift 2) · Mathematics

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

Solution

$2 x + 3 y + 2 z = 9 . . . (1)$

$3 x + 2 y + 2 z = 9 . . . (2)$

$x - y + 4 z = 8 . . . (3)$

$(1) - (2) \Rightarrow - x + y = 0 \Rightarrow x - y = 0$

from $(3) 4 z = 8 \Rightarrow z = 2$

from $(1) 2 x + 3 y = 5$

$\Rightarrow x = y = 1$

$∴$ system has unique solution.

Hence, the correct answer is option: 'B'.