Find the value of k for which the following system of equations has infinite solutions: 4x + 2y - (k + 2) = 0 and 2x + y - 3 = 0

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Solution

The correct option is D 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 have infinite solutions if $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}},$

Thus, for the given pair of equations to have infinte solutions,
$\frac{4}{2} = \frac{2}{1} = \frac{- (k + 2)}{- 3}$
$\Rightarrow \frac{(k + 2)}{3} = 2$
$\Rightarrow k = 4$

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