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Question

Find the value of k for which the following system of equations has a unique solution:
4x+ky+8=0x+y+1=0

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Solution

The given system of equations is
4x+ky+8=0 .....ix+y+1=0 .....ii
This system is of the form
a1x+b1y+c1=0a2x+b2y+c2=0
where a1=4, b1=k, c1=8 and a2=1, b2=1, c2=1
For the given system of equations to have a unique solution, we must have
a1a2b1b241k1k4
Hence, k4.

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