Question

Find the value of c for which the system
cx + 3y = c - 3, 12x + cy = c has infinitely many solutions.

• A. 6
• B. 8
• C. 4
• D. 2
• E. None of these

Answer 1

The correct option is A 6

For the equation, cx + 3y = c - 3 and 12x + cy = c to have an infinite number of solutions we must have,
$\frac{c}{12}=\frac{3}{c}=\frac{(c-3)}{c}\Rightarrow \frac{c}{12}=\frac{3}{c}$ and $\frac{c}{12}=\frac{(c-3)}{c}$
$\Rightarrow c^2=36$ and $c^2=12c-36$
$\Rightarrow c=\pm 6$ and $(c-6{)}^2=0$
$\Rightarrow c=\pm 6$ and $c=6$
$\Rightarrow c=6$