Choose the correct answer from the given four options:
Graphically, the pair of equations
$6 x-3 y+10=0$
$2 x-y+9=0$
represents two lines which are
(A) intersecting at exactly one point.
(B) intersecting at exactly two points.
(C) coincident.
(D) parallel.

Given:

Given pair of linear equations is:

$6x\ -\ 3y\ +\ 10\ =\ 0$

$2x\ -\ y\ +\ 9\ =\ 0$

To do:

We have to find the correct option.

Solution:

Comparing the given pair of linear equations with the standard form of linear equations $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$, we get,

$a_1=6, b_1=-3$ and $c_1=10$

$a_2=2, b_2=-1$ and $c_2=9$

Here,

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

$\frac{b_1}{b_2}=\frac{-3}{-1}=3$

$\frac{c_1}{c_2}=\frac{10}{9}$

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

Therefore, graphically the two lines are parallel to each other.