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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 ` `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 .
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