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 `             `3/c=(3-c)/-c`

⇒`c/12=3/c`              or             ⇒ c(c-6)=0

⇒ c² = 36                                 ⇒c = 0, 6 

⇒ c = ± 6
Hence the value of c = 6 .