If ad is not equal to bc, then find whether the pair of linear equation ax+by =p and cx+dy=q has no solution, unique solution or infinitely many solutions.

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Solution

ax + by - p = 0....(1)

cx + dy - q = 0....(2)

from the equations we get a1 = a, a2 = c, b1 = b, b2 = d, c1 = -p, c2 = -q

so a1/a2 = a/c

b1/b2 = b/d

c1/c2 = -p/-q or p/q

Equating the following

a/c = b/d

by cross multiplication

ad = bc

but in question it is given ad is not equal to bc

so a1/a2 is not equal to b1/b2

so it is a unique solution

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