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Question
Find c if the system of equations cx + 3y + (3 – c) = 0; 12x + cy – c = 0 has infinitely many solutions?
Solution
cx + 3y + (3 - c) = 0 ....(i)
12x + cy - c = 0 ....(ii)
For infinitely many solutions, `("a"_1)/("a"_2) = ("b"_1)/("b"_2) = ("c"_1)/("c"_2)`
`=> "c"/12 = 3/"c" = (3-"c")/"-c"`
`=> "c"/12 = 3/"c"`
`=> "c"^2 = 36`
`=> "c" = +- 6`
OR
`3/"c" = (3-"c")/"-c"`
`=> "c"("c" - 6) = 0`
`=> "c" = 0,6`
Hence, c = 6 is the solution which gives infinitely many solution.
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