Question

The number of values of k for which the system of equations

                (k + 1) x + 8y = 4k

                kx + (k + 3) y = 3k – 1

has infinitely many solution is

Solution

Correct option is

0

For infinitely many solutions, Δ = 0, and Δ1 = 0, Δ2 = 0

Δ = 0 ⇒ (k  + 1) (k + 3) – 8k = 0

k2 – 4k + 3 = 0  ∴ k = 3,1

Δ1 = 0 ⇒ k2 – 3k + 2 = 0 or k = 1,2

Δ2 = 0 ⇒ k = 1

Hence k – 1 is only value for which each Δ, Δ1, Δ2 is zero.

SIMILAR QUESTIONS

Q1

The system of equations

            ax + ayz = 0

            bxy + bz = 0

         – x + cy + cz = 0

(where a, b, c ≠ – 1 )has a non – trivial solution, then value of

          

Q2

The values of λ for which the system of equations

(λ + 5)x + (λ – 4)y + z = 0

(λ – 2)x + (λ + 3)y + z = 0

                 λx + λy + z = 0

has a non – trivial solution is (are)

Q3

Number of real values of λ for which the system of equations

(λ + 3)x + (λ + 2)y + z = 0

        3x + (λ + 3)y + z = 0

                 2x + 3y + z = 0

has a non – trivial solution is

Q4

The values of λ for which the system of equations

                2x + y + 2z = 2,

                  x – 2y + z = – 4

                  x + y + λz = 4

has no solution is

Q5

Evaluate the determinant without expansion as for as possible.

                          

Q6
Q8

 

Then f (100) is equal to

 

Q9
Q10

For what real values of k, the system of equations x + 2y + z = 1; x + 3y + 4z = k; x + 5y + 10z = khas solution? Find the solution of each case.