Question

if the equation 8x+5y+11=0 and 20x+ky-9=0 have no solution,then the find the k value​

Answer 1

Answer:

Step-by-step explanation:

For no solution, a1/a2 = b1/b2 ≠ c1/c2

= 8/20 = 5/k ≠ 11/-9

= 8k = 100 and 11k ≠ -45

= k = 100/8 = 12.5

Answer 2

Step-by-step explanation:

Given :-

8x+5y+11=0 and 20x+ky-9=0 have no solution.

To find :-

Find the value of k ?

Solution :-

Given pair of linear equations in two variables are 8x+5y+11 = 0

On comparing with a1x+b1y+c1 = 0 then

a1 = 8

b1 = 5

c1 = 11

and

20x+ky-9 = 0

On comparing with a2x+b2y+c2 = 0 then

a2 = 20

b2 = k

c2 = -9

Given that

Equations have no solution

We know that

If a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 have no solution,if a1/a2 = b1/b2

=> 8/20 = 5/k

=> 2/5 = 5/k

On applying cross multiplication then

=> 2×k = 5×5

=> 2k = 25

=> k = 25/2

Therefore, k = 25/2

Answer:-

The value of k for the given problem is 25/2

Used formulae:-

If a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 have no solution,if a1/a2 = b1/b2

Points to know:-

If a1x+b1y+c1 = 0 and a2x+b2y+c2 = 0 are pair of linear equations in two variables then,

→ If a1/a2 = b1/b2 then they are inconsistent or parallel lines with no solution.

→ If a1/a2 ≠ b1/b2 then they are consistent and Independent or intersecting lines with only one solution.

→ If a1/a2 = b1/b2 = c1/c2 then they are consistent and dependent or Coincident lines with so many solutions .