Question

The value of k for which the system of equations
x + 2y = 5
3x + ky + 15 = 0
has no solution is
A. 6
B. – 6
C. 3/2
D. None of these

Answer 1

Answer:

The value of

for which the system of equations

has no solution is (a)

(b)

(c)

(d) None of these

Answer 2

Given :  System of equations has no solution  

x + 2y = 5

3x + ky + 15 = 0  

 

Concept :

If a pair of linear  equations is given by

a1x  +  b1y  +  c1 = 0

a2x  +  b2y  +  c2 = 0

System has no solution and such pair of linear equation is inconsistent pair of  linear equations

For parallel lines (inconsistent) :

a1 /a2 = b1/b2 ≠ c1/ c2

 

SOLUTION:

We can write the Given pair of  linear equation as :

x + 2y - 5 = 0…………(1)

3x + ky + 15 = 0……………..(2)

On comparing with General form of a pair of linear equations  in two variables x & y is:

a1x + b1y + c1 = 0  and   a2x + b2y + c2= 0

a1 = 1 , b1 = 2, c = - 5

a2 = 3 , b2 = k , c = 15

We have ,  

a1/a2 = 1/3 ,  b1/b2 =  2/k , c1/c2 = - 5/15 = -1/3

 

Given: A pair of linear equations has no Solution, then  

a1 /a2 = b1/b2 ≠ c1/ c2

1/3 = 2/k ≠ -1/3

(I)        (II)        (III)

 

On  taking I & II terms  :

1/3 = 2/k

k = 2 × 3

k = 6

Hence,the value of k is 6.

The correct option is (A) : 6

HOPE THIS ANSWER WILL HELP YOU……

 

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