Question

The graphic representation of the pair of equations $2x+4y-15=0$ and $x+2y-4=0$ gives a pair of

• A. Parallel lines
• B. Intersecting lines
• C. Coincident lines
• D. None of these

Answer 1

The correct option is A Parallel lines

The equations are
$2x+4y-15=0$
$x+2y-4=0$
Here, $a_1=2,b_1=4,c_1=-15$
and $a_2=1,b_2=2,c_2=-4$
$\frac{a_1}{a_2}=\frac{2}{1}=2$
$\frac{b_1}{b_2}=\frac{4}{2}=2$
$\frac{c_1}{c_2}=\frac{-15}{-4}$
$\Rightarrow \frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
$\Rightarrow$ The system of equations has no solution.
$\therefore$ Graphical representation of the given pair of equations is parallel lines