Question

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

Answer 1

Answer:

5

Step-by-step explanation:

x+2y=3

5x+ky=-7

Therefore,

a1=1 , b1=2 , c1=3

a2=5 , b2=k , c2=-7

Since the linear equation is inconsistent , so it will have a unique solution.

so,

a1/a2 is not equal to b1/b2

b1/b2 is not equal to c1/c2

so,

1/5 is not equal to 2/k .k is not equal to 10 ( by cross multiplication method)

2/k is not equal to 3/-7.therefore -14 /3 is not equal to k . hence the correct answer is 5

Answer 2

Given: The system of linear equations x+2y=3, 5x+ky+7=0 is inconsistent.

To find: The value of k.

Solution:

A system of linear equations is said to be inconsistent when it has no solution. The condition for inconsistency is given as follows.

$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b__{2}}$

The first linear equation can be rearranged and written as x+2y-3=0. For the given linear equations, a₁, b₁, c₁ and a₂, b₂, c₂ is 1, 2, -3 and 5, k, 7, respectively. Now, the values are substituted in the condition and the value of k is calculated as follows.

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

$k = 10$

Therefore, the value of k is 10.