Question: Lines $ax -3y=5$ and $4x -2y = 3$ are parallel to each other. Find the value of a.


Solution:
Given,

Equation of line (i) = $ax -3y =5$

Slope of line (i), $(m_1) = - \dfrac{coefficient\; of \;x}{coefficient\;of\;y}$
$= - \dfrac{a}{-3}$
$= \dfrac{a}{3}$

Equation of line (ii) = $4x -2y = 3$

Slope of line (ii), $(m_2) = -\dfrac{coefficient\; of \;x}{coefficient\;of\;y}$
$= - \dfrac{4}{-2}$
$= 2$

We know,

When two lines are parallel, their slopes are equal
i.e. $m_1 = m_2$

$or, \dfrac{a}{3} = 2$

$or, a = 2×3$

$\therefore a = 6$

Hence, the value of a is 6 in the above equation of line.


Related Notes and Solutions:

Here is the website link to all the important formulae of Coordinate Geometry of Class 10.

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