81
(a) Find the value of $c$ for which the following pair of linear equations has infinitely many solutions :
$cx + 3y = c - 3$
$12x + cy = c$
OR
(b) Solve for $x$ and $y$ :
$3x + 2y = 65$
$2x + 3y = 60$
$cx + 3y = c - 3$
$12x + cy = c$
OR
(b) Solve for $x$ and $y$ :
$3x + 2y = 65$
$2x + 3y = 60$
Show SolutionHide Solution↓
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]
OR
(b) Solving the given equations to get $x = 15$ [1 mark]
and $y = 10$ [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]
OR
(b) Solving the given equations to get $x = 15$ [1 mark]
and $y = 10$ [1 mark]