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Question

Find the value of k for which each of the following systems of equations has no solution:

kx+3y=3,12x+ky=6.


A
k = 6
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B
k = -6
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C
k = -3
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D
k = 3
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Solution

The correct option is B k = -6

Equations are written as

kx + 3y – 3 = 0 .....(1)

12x + ky – 6 = 0 ....... (2)

a1=k, b1=3, c1=3

a2=12, b2=k, c2=6

for no solution we must have:

a1a2=b1b2c1c2

Now,

k12=3k36

k12=3k
and
3k12

k2=36,k6

Hence, k = -6

Hence, the given system of equations is has no solution if k =-6.


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