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Find the value of $c$ for which the following pair of linear equations has infinitely many solutions :
$cx + 3y = c - 3$
$12x + cy = c$
$cx + 3y = c - 3$
$12x + cy = c$
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Solution: (a) $\frac{c}{12} = \frac{3}{c} = \frac{c-3}{c}$ [1 mark]
$\Rightarrow c^2 = 36$ and $c^2 - 6c = 0$ [1/2 mark]
$\Rightarrow c = \pm 6$ and $c = 0, 6$
$\therefore c = 6$ [1/2 mark]
$\Rightarrow c^2 = 36$ and $c^2 - 6c = 0$ [1/2 mark]
$\Rightarrow c = \pm 6$ and $c = 0, 6$
$\therefore c = 6$ [1/2 mark]