Question

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Answer 1

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Answer 2

$\large\mathcal{\underbrace{\red{SOLUTION:-}}}$

GIVEN :-

✍️ The pair of linear Equation are

• kx - 4y = 3 -------(1)

• 6x - 12y = 9 --------(2)

✍️ Here,

$\checkmark\:\rm{\purple{a_1\:=\:k\:,\:b_1\:=\:-4\:,\:c_1\:=\:3\:}}$

$\checkmark\:\rm{\blue{a_2\:=\:6\:,\:b_2\:=\:-12\:,\:c_2\:=\:9\:}}$

CALCULATION :-

✍️ For infinitely many solution,

$\bigstar\:\rm{\orange{\boxed{\dfrac{a_1}{a_2}\:=\:\dfrac{b_1}{b_2}\:=\:\dfrac{c_1}{c_2}\:}}}$

$\rm{\implies\:\dfrac{k}{6}\:=\:\dfrac{-4}{-12}\:=\:\dfrac{3}{9}\:}$

$\rm{\implies\:\dfrac{k}{6}\:=\:\dfrac{1}{3}\:=\:\dfrac{1}{3}\:}$

$\rm{\implies\:\dfrac{k}{6}\:=\:\dfrac{1}{3}\:}$

$\rm{\implies\:3k\:=\:6\:}$

$\rm{\green{\implies\:k\:=\:2\:}}$

✍️ Therefore, the given system of equation has infinitely many solution, if ‘k = 2’ .