Question

What is the value of ‘k’ for which the graph of the equations 2x - 3y = 9 and kx - 9y = 18 are parallel

lines?​

Answer 1

$\huge\mathcal{\fcolorbox{cyan}{black}{\pink{ANSWER}}}$

If the two linear equation are parallel then,

$\frac{2}{k} = \frac{ - 3}{ - 9} \\ \implies \: k = \frac{2 \times ( - 9)}{ - 3} = 6$

Answer 2

$\huge\mathtt\pink{A}\mathtt\red{N}\mathtt\blue{S}\mathtt\green{W}\mathtt\purple{E}\mathtt\green{R}$

$\\: \: \: \: \: \: \: \rightarrow \mathtt \red{for \: being \: parallel \: lines \: should \: follow \: }$

$\huge\mathtt \green{\frac{a1}{b1} = \frac{a2}{b2} ≠ \frac{c1}{c2} }$

Hence

$\\: \: \: \: \: \: \: \: \rightarrow \mathtt \ \frac{2}{k} = \frac{ - 3}{ - 9} ≠ \frac{1}{2}$

$\\: \: \: \: \: \: \: \: \rightarrow \mathtt \ \frac{2}{k} = \frac{ - 3}{ - 9}$

$\\: \: \: \: \: \: \: \: \rightarrow \mathtt \ \frac{2}{k} = \frac{ 1}{ 3}$

$\\: \: \: \: \: \: \: \: \huge\rightarrow \mathtt \blue{ \fbox{ k = 6}}$