Question

Question 2 (i)
Do the following equations represent a pair of coincident lines? Justify your answer.
$3x+\frac{1}{7}y=3and7x+3y=7$

Answer 1

For lines to be coincident,

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

The given pair of linear equations are:

$3x+\frac{y}{7}-3=0$

and 7x + 3y – 7 = 0

$where{a}_1=3,b_1=\frac{1}{7},c_1=-3a_2=7,b_2=3,c_2=-7now,\frac{a_1}{a_2}=\frac{3}{7},\frac{b_1}{b_2}=\frac{1}{21},\frac{c_1}{c_2}=\frac{3}{7}$

Here, $\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$

Thus, the given pair of equations does not represent coincident lines.