Question

The value of K for which the system of linear equations x +2y = 3 , 5x +ky +7 = 0 is inconsistent is :



14

2

5

10​

Answer 1

Step-by-step explanation:

Since the following pair of lines are inconsistent then these lines are Parallel in nature.

Then,

a1=1, b1=2,c1=-3

a2=5,b2=k,c2=7

For parallel lines we have,

a1/a2=b1/b2 is not equal to c1/c2.

For a1/a2=b1/b2

=>1/5=2/k

=>k=10.

Therefore the value of k for which the following pair of eqn is inconsistent is K=10

Answer 2

The value of k for which the system of the given linear equations is inconsistent is option (d) 10.

Solution: A pair of linear equations is inconsistent when there is no solution to the pair of linear equations. No value of x and y can satisfy an inconsistent solution.

The two equations given here are x+2y=3 and 5x+ky+7=0.

x+2y=3 can be written as x+2y-3=0

For a pair of linear equations ax+by+c=0 and px+qy+r=0 to be inconsistent, the necessary condition is:

$\frac{a}{p} = \frac{b}{q} ≠ \frac{c}{r}$

Here, a= 1, b=2, c= -3, p= 5, q= k ,c= 7

Now,

$\frac{a}{p} = \frac{b}{q}$

$= > \frac{1}{2} = \frac{5}{k}$

=> k = 5 × 2

=> k= 10

Also, c/r= -3/7 which is not equal to a/b.

Therefore, for k= 10, the system of linear equations is inconsistent.