Question

Do the following equations represent a pair of coincident lines? Justify your answer.

$x+\frac{1}{7}y=37$ and $x+3y=7$

• A. No
• B. Yes
• C. Cannot be determined
• D. None of these

Answer 1

The correct option is A No

$x+\frac{1}{7}y=37$ and $x+3y=7$
The following equation can be written as
$x+\frac{1}{7}y-37=0$ and $x+3y-7=0$
Here, $a_1=1,b_1=\frac{1}{7},c_1=-37$ and $a_2=1,b_2=3,c_2=-7$
$\frac{a_1}{a_2}=\frac{1}{1},\frac{b_1}{b_2}=\frac{\frac{1}{7}}{3},\frac{c_1}{c_2}=\frac{-37}{-7}$
Hence, $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}\ne \frac{c_1}{c_2}$
So, the given equations do not represent a pair of coincident lines.