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

The following system of linear equations
2x+3y+2z=9
3x+2y+2z=9
x-y+4z=8
  1. has infinitely many solutions
  2. has a unique solution
  3. has a solution α,β,γ satisfying α+β2+γ3=12
  4. does not have any solution

Solution

2x+3y+2z=9   ...1

3x+2y+2 z=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

∴ system has unique solution.

Asked in: JEE Main 2021 (25 Feb Shift 2)

Practice more Determinants questions on Aicharya