Question

find the value of k for which the system of equation x +3y =4 and 2x+ky =7 is inconsistent.​

Answer 1

Answer:

from above two equation:

a1 =1;b1=3; c1=-4

a2 = 2 ;b2=k ;c2=-7

than.. a1/a2= b1/b2= c1/c2

1/2=3/k=-4/-7

1/2=3/k

k=6

Answer 2

Answer:

The value of k for which the system of equation x +3y =4 and 2x+ky =7 is inconsistent = 6

Step-by-step explanation:

Given,

The system of equation x +3y =4 and 2x+ky =7 is inconsistent.​

To find,

The value of 'k'

Recall the concept,

A pair of linear equations a₁ +b₁y +c₁ =  0 and a₂x+b₂y+c₂ = 0 are said to be inconsistent, if they have no solution and the two lines are parallel.

That is if  $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$ ---------------(1)

Solution:

We have the equations  x +3y =4 and 2x+ky =7

Comparing the given equations with a₁ +b₁y +c₁ =  0 and a₂x+b₂y+c₂ = 0 we get

a₁ = 1, b₁ = 3 and c₁ = -4

a₂ = 2, b₂ = k and c₂ = -7

Since the given system of equations x +3y =4 and 2x+ky =7 is consistent,

from condition (1) we get

$\frac{1}{2} = \frac{3}{k} \neq \frac{-4}{-7}$

$\frac{1}{2} = \frac{3}{k}$ ⇒ k = 6

The value of k = 6

∴The value of k for which the system of equation x +3y =4 and 2x+ky =7 is inconsistent = 6

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