The graphic representation of the equations $x+2 y=3$ and $2 x+4 y+7=0$ gives a pair of (a) parallel lines (b) intersecting lines (c) coincident lines (d) none of these

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The graphic representation of the equations $x+2 y=3$ and $2 x+4 y+7=0$ gives a pair of
(a) parallel lines
(b) intersecting lines
(c) coincident lines
(d) none of these

The graphic representation of the equations $x+2 y=3$ and $2 x+4 y+7=0$ gives a pair of
(a) parallel lines
(b) intersecting lines
(c) coincident lines
(d) none of these

Answer: (a) parallel lines

Solution:
The given system can be writlen us follows:
$x+2 y-3=0$ and $2 x+4 y+7=0$
Given equations are of the following form:
$a_{1} x+b_{1} x+c_{1}=0$ and $a_{2} x+b_{2} y+c_{2}=0$
Here, $a_{1}=1, b_{1}=2, c_{1}=-3$ and $a_{2}=2, b_{2}=4$ and $c_{2}=7$
$\therefore \frac{a_{1}}{a_{2}}=\frac{1}{2}, \frac{h_{1}}{b_{2}}=\frac{2}{4}=\frac{1}{2}$ and $\frac{c_{1}}{c_{2}}=\frac{-3}{7}$
$\therefore \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$
Therefore the given system has no solution.
As a result, the lines are parallel.