Question

For what value of k the following system of equations will be inconsistent.kx+2y-5=0; 8x + ky-10=0​

Answer 1

Answer:

a1/a2 = b1/b2 isn't equal to c1/c2

Step-by-step explanation:

k/8 = 2/k isn't equal to-5/-10

so, k ^2 = 16 and isn't equal to 1/2

or k = +4 or -4 which already don't equals to 1/2

hence,value of k = +4 or -4

Answer 2

The value of k = 4

Given:

kx + 2y - 5 = 0

8x + ky - 10 = 0​  are pair of lines

To find:

The value of k

Solution:

Note: When two lines a₁x +b₁y +c₁ = 0 and a₂x +b₂y +c₂ = 0 are inconsistent then

               a₁/a₂ = b₁/b₂ ≠ c₁/c₂  

Now using above data we will solve the given question

Compare given line kx + 2y - 5 = 0 with a₁x +b₁y +c₁ = 0

⇒ a₁ = k, b₁ = 2 and  c₁ = -5

Compare given line 8x + ky - 10 = 0​ with a₂x +b₂y +c₂ = 0

⇒ a₂ = 8,  b₂ = k  and c₂ = -10

As we know given lines are inconsistent

⇒  k /8 = 2/k ≠ -5 /-10

Take  k /8 = 2/k  

⇒ k² = 16

⇒ k² = 4 × 4  

⇒ k = 4

Therefore,

The value of k = 4

#SPJ2