Question

8. Find a relation between a and b, for which
the system of equations ax + 2y = 7 and 3x +
by = 16 represents parallel lines.
​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Parallel lines are}$

$\mathsf{ax+2y=7\;\&\;3x+by=16}$

$\underline{\textbf{To find:}}$

$\textsf{The relation between a and b}$

$\underline{\textbf{Solution:}}$

$\underline{\textbf{Concept used:}}$

$\boxed{\textsf{If two lines are parallel, their slopes are equal}}$

$\mathsf{Slope\;of\;ax+2y=7\;is\;m_1=\dfrac{-a}{2}}$

$\mathsf{Slope\;of\;3x+by=16\;is\;m_2=\dfrac{-3}{b}}$

$\mathsf{As\;per\;given\;data,\;m_1=m_2}$

$\implies\mathsf{\dfrac{-a}{2}=\dfrac{-3}{b}}$

$\implies\boxed{\mathsf{ab=6}}$

$\textsf{which is the required relation}$

$\underline{\textbf{Find more:}}$

If the lines represented by 3x+2y+5=0 and kx-6y+4=0 are parallel, then k =  

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