# Find C If the System of Equations Cx + 3y + (3 – C) = 0; 12x + Cy – C = 0 Has Infinitely Many Solutions? - Mathematics

Sum

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.

Concept: Quadratic Equations Examples and Solutions
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