By the graphical method,find whether the following pair of equations are consistent or not. If consistent,solve them.
$x - 2y = 6$
$3x - 6y = 0$

(D) The given pair of equations is:
$x - 2y = 6$ ..... $(i)$
$3x - 6y = 0$ ..... $(ii)$
Comparing these with the standard form $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$,we get:
$a_1 = 1, b_1 = -2, c_1 = -6$
$a_2 = 3, b_2 = -6, c_2 = 0$
Now,calculating the ratios:
$\frac{a_1}{a_2} = \frac{1}{3}$
$\frac{b_1}{b_2} = \frac{-2}{-6} = \frac{1}{3}$
$\frac{c_1}{c_2} = \frac{-6}{0}$ (which is undefined)
Since $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$,the lines represented by these equations are parallel to each other.
Because the lines are parallel,they do not intersect at any point.
Therefore,the given pair of linear equations is inconsistent and has no solution.