Question

The pair of linear equations 2x + 5y = 3 and 6x + 15y = 12 represent

• A. intersecting lines
• B. parallel lines
• C. coincident lines
• D. none of these

Answer 1

Answer: (B)

parallel lines

The equation can be written as

$2x+5y-3=0$ and $6x+15y-12=0$

Here $a_1=2,b_1=5,c_1=-3$ and $a_2=6,b_2=15,c_2=-12$

$\frac{a_1}{a_2}=\frac{2}{6}=\frac{1}{3}$

$\frac{b_1}{b_2}=\frac{5}{15}=\frac{1}{3}$

$\frac{c_1}{c_2}=\frac{-3}{-12}=\frac{1}{4}$

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

Hence the given pair of linear equation represents parallel line.