Question

Graphically, the pair of equations $6x-3y+10=0,2x-y+9=0$ represents two lines which are

• A. Intersecting at exactly one point
• B. Intersecting at exactly two points
• C. Coincident
• D. Parallel

Answer 1

The correct option is D Parallel

The linear equations are
$6x-3y+10=0$
$2x-y+9=0$
Here, $a_1=6,b_1=-3,c_1=10$
$a_2=2,b_2=-1,c_2=9$
$\therefore \frac{a_1}{a_2}=\frac{6}{2}=3$
$\frac{b_1}{b_2}=\frac{-3}{-1}=3$
$\frac{c_1}{c_2}=\frac{10}{9}$
$\Rightarrow \frac{a_1}{a_2}=\frac{b_2}{b_2}\ne \frac{c_1}{c_2}$
$\therefore$ The lines represented by the given equations are parallel.