Question

Find c if the system of equations cx + 3y + (3 – c) = 0; 12x + cy – c = 0 has infinitely many solutions?

Answer 1

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.