Find the valueof k for which the following system of equations has no solution:
2x + 3y - 5 = 0 and kx + 6y - 8 = 0

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Solution

The correct option is C 4
Given two equations $a_{1} x + b_{1} y = c_{1} a n d a_{2} x = b_{2} y = c_{2},$
the pair of equations will not have a solution if $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}},$

Thus, for the given pair of equations to have no solution,
$\frac{2}{k} = \frac{3}{6} = \frac{- 5}{- 8}$
$\Rightarrow \frac{2}{k} = \frac{1}{2} \neq \frac{5}{8}$
$\Rightarrow k = 4$

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