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Question 4 (iv)
Find the values of p for the following pair of equations 2x + 3y – 5 = 0 and px – 6y – 8 = 0, if the pair of equations has a unique solution.

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Solution

Pair of equations is
2x+3y5=0 ...(i)
px6y8=0 ...(ii)
Pair of equations have unique solution if
a1a2b1b2
Here, a1=2, b1=3 and
a2=p,b2=6
2p36
3p2×6
p123
p4
Hence, the system of linear equations has unique solution for all real values of p except -4.

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