Question

for what value of k, do the equations 2x – 3y + 10 = 0 and 3x + ky + 15 = 0 represent coincident lines




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Answer 1

$\boxed{ \boxed{ \underline{\underline{\footnotesize \sf \purple{ Solution:-}}}}}$

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$\footnotesize \sf{2x - 3y + 10 = 0}$

$\footnotesize \sf{3x + ky + 15= 0}$

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$\footnotesize \sf \purple{As \: the \: line \: coincide \: they \: have \: infinitely \: many \: solutions.}$

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$\purple \bullet\footnotesize \sf {\:a1 = 2}$

$\purple \bullet\footnotesize \sf {\: a2 = 3}$

$\purple \bullet\footnotesize \sf{\: b1= - 3}$

$\purple \bullet\footnotesize \sf{\: b2= k}$

$\purple \bullet \footnotesize \sf{\: c1= 10}$

$\purple \bullet\footnotesize \sf{\: c2= 15}$

$\: \: \: \: \: \: \: \: \: \: \: \:$

$\footnotesize\sf{ \frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2} }$

$\footnotesize \sf{ \frac{2}{3} = \frac{ - 3}{k} = \frac{10}{15} }$

$\footnotesize \sf{ \frac{ - 3}{k} = \frac{2}{3} }$

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$\footnotesize\sf \purple{Do \: Cross \: Multiplication }$

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$\footnotesize \sf{ k = \frac{ - 9}{2} }$

$\footnotesize \sf { k = \cancel \frac{ - 9}{2} }$

$\boxed{ \boxed{ \underline{\underline{\footnotesize \sf \purple{ k = - 4.5}}}}}$