Question

The following system of linear equations

2x + 3y + 2z = 9

3x + 2y + 2z = 9

x - y + 4z = 8

(1) has a solution (a, b, g) satisfying α + β² + γ³ = 12

(2) has infinitely many solutions

(3) does not have any solution

(4) has a unique solution

Answer 1

Correct option is (4) has a unique solution

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

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

x - y + 4z = 8 ...(3)

(1) - (2) ⇒ -x + y = 0 ⇒ x - y = 0

from (3) 4z = 8 ⇒ z = 2

from (1) 2x + 3y = 5

⇒ x = y = 1

\(\therefore\) system has unique solution