Question

find the value of k in which the following each system of linear equation has no solution 2x+5y-3=0,8x+ky-10=0​

Answer 1

Step-by-step explanation:

Given:-

2x+5y-3=0

8x+ky-10=0

The system of linear equation has no solution.

To find:-

Find the value of k ?

Solution:-

Given pair of linear equations in two variables are

2x+5y-3=0----------(1)

On Comparing this with a1x+b1y+c1=0

a1=2 ,b1=5 and c1=-3

8x+ky-10=0----------(2)

On Comparing this with a2x+b2y+c2=0

a2 = 8, b2=k and c2=-10

Given that

The system of linear equation has no solution

We know that

The system of linear equation has no solution if a1/a2=b1/b2≠c1/c2

=> 2/8=5/k≠-3/-10

=> 2/8=5/k

On applying cross multiplication then

=> k×2 = 8×5

=> 2k = 40

=>k = 40/2

=> k=20

Answer:-

The value of k for the given problem is 20

Used formula:-

• The system of linear equations a1x+b1y+c1=0 and a2x+b2y+c2=0 has no solution if a1/a2=b1/b2≠c1/c2
• The lines are inconsistent lines or parallel lines