Question

The graphical representation of the pair of equations $x+by-4=0$ and $2x+by-12=0$, represents:

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

Answer 1

The correct option is A intersecting lines

For the given pair of equations $x+by-4=0$ and $2x+by-12=0$;

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

$\frac{b_1}{c_2}=\frac{b}{b}=1$

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

As the given pair of linear equation satisfies -

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

The graph will be a pair of lines intersecting at a unique point.