If the system of linear equations 2 x + y - z = 7 x - 3 y + 2 z = 1 x + 4 y + δ z = k , where δ ,…

If the system of linear equations
2x+y-z=7
x-3y+2z=1
x+4y+δz=k, where δ,k∈R
has infinitely many solutions, then δ+k is equal to
  1. -3
  2. 3
  3. 6
  4. 9

Solution

For infinitely many solutions, ∆=21-11-3214δ=0

⇒δ=-3

and ∆1=71-11-32K4-3=0⇒k=6

⇒δ+K=3

Asked in: JEE Main 2022 (29 Jun Shift 1)

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