Question

Consider two equations in the variables x and y written in the standard form:
$5x+6y+4=0and$
$10x+12y+7=0$
What is the nature of these two lines?

• A. Coincident
• B. Intersecting
• C. Parallel
• D. Coincident or parallel

Answer 1

The correct option is C Parallel

The equations of the two lines are:

$5x+6y+4=0$
$10x+12y+7=0$

Here,
$a_1=5,b_1=6,c_1=4,a_2=10,b_2=12,c_2=7$.

$\frac{a_1}{a_2}=\frac{5}{10}=\frac{1}{2}$

$\frac{b_1}{b_2}=\frac{6}{12}=\frac{1}{2}$

$\frac{c_1}{c_2}=\frac{4}{7}$.

$\Rightarrow \frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$.

$\Rightarrow$ The pair of equations have no solutions, i.e, they are parallel.

Also, when we plot the graphs of these two equations, it is visible that they are parallel to each other.