Question

If a pair of linear equations 2x+ky=7 and 3x-9y=12 is consistent and independent, then the value(s)of K is(are)​

Answer 1

Answer:

it should be k is not equal to -6

Answer 2

The value of k ∈ R - {-6}.

If a pair of linear equations 2x + ky = 7 and 3x - 9y = 12 is consistent and independent.

We have to find the value(s) of K.

First we should understand what is the meaning of consistent and independent and some related terms.

1. consistent independent ⇒ only one solution (intersecting lines)
2. consistent dependent ⇒infinite solutions (same lines)
3. inconsistent ⇒no solution (parallel lines)

Concept : We know, If a pair of linear equations of two variables is given ;

i.e., a₁x + b₁y = c₁ and a₂x + b₂y = c₂

for unique solution ⇒a₁/a₂ ≠ b₁/b₂

for infinitely many solutions ⇒a₁/a₂ = b₁/b₂ = c₁/c₂

for no solution ⇒a₁/a₂ = b₁/b₂

∴ for unique solution (consistent independent) , a₁/a₂ ≠ b₁/b₂

here, a₁ = 2 , a₂ = 3 , b₁ = k and b₂ = -9

⇒2/3 ≠ k/-9

⇒k ≠ -6

Therefore the value of k ∈ R - {-6}.