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Question 2
For which value (s) of k will the pair of equations
kx + 3y = 5 – 3,
12x + 5y = k
has no solution?

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Solution

Given pair of linear equations is
kx + 3y = k – 3
and 12x + ky = k
on comparing with ax + by + c = 0 we get
a1=k,b1=3 and c1=1(k3)a2=12, b2=k and c2=k
For no solution of the pair of linear equations
a1a2=b1b2c1c2k12=3k(k3)k
Tasking first two parts we get
k12=3kk2=36k=±6
Taking last two parts, we get
3kk3k3kk(k3)3kk(k3)0k(3k+3)0k0 and k6
Hence, required value of k for which the given pari of linear equations has no solutions is – 6

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