Question

The graphical representation of the pair of equations $x+2y-4=0$ and $2x+4y-12=0$ is:

• A. intersecting lines
• B. parallel lines
• C. coincident lines
• D. all the above

Answer 1

Answer: (B)

parallel lines

For two lines to be parallel,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$ -----equation$\left(1\right)$

where, $a$ and $b$ are coefficients of $x$ and $y$ and $c$ is constant

Here, the lines are $x+2y-4=0$ and $2x+4y-12=0$
$a_1=1,b_1=2,c_1=-4$ and $a_2=2,b_2=4,c_2=-12$

As we can see that,

$\frac{1}{2}=\frac{2}{4}\ne \frac{-4}{-12}$

We can say that the given lines are parallel.