The value of k ∈ R , for which the following system of linear equations 3 x - y + 4 z = 3 x + 2 y - 3…

The value of k∈R, for which the following system of linear equations

3x-y+4z=3

x+2y-3z=-2

6x+5y+kz=-3

has infinitely many solutions, is:

  1. 3
  2. -5
  3. 5
  4. -3

Solution

We have,

3x-y+4z=3

x+2y-3z=-2

6x+5y+kz=-3

For infinitely many solutions,

A=0

⇒3-1412-365 k=0

⇒3(2k+15)+1k+18+45-12=0

⇒3(2k+15)+k+18-28=0

⇒7k+35=0

⇒k=-5

Asked in: JEE Main 2021 (20 Jul Shift 2)

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