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Question

The pair of linear equations 4x − 5y −20 = 0 and 3x + 5y − 15 = 0 has
(a) a unique solution
(b) two solutions
(c) many solutions
(d) no solution

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Solution

(a) a unique solution
The given equations are of the form a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, where
a1 = 4, b1 = - 5, c1 = - 20 and a2 = 3, b2 = 5 and c2 = - 15
a1a2=43, b1b2=-55 and c1c2=-20-15=43
∴ These graph lines will intersect at a unique point, when a1a2b1b2.
Hence, the given system has a unique solution.

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