Which of the following pairs of linear equations has a unique solution,no solution,or infinitely many solutions? In case there is a unique solution,find it by using the cross-multiplication method.
$3x - 5y = 20$
$6x - 10y = 40$

(D) Given equations are:
$3x - 5y - 20 = 0$ --- $(1)$
$6x - 10y - 40 = 0$ --- $(2)$
Comparing these with the standard form $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$,we get:
$a_1 = 3, b_1 = -5, c_1 = -20$
$a_2 = 6, b_2 = -10, c_2 = -40$
Now,calculating the ratios:
$\frac{a_1}{a_2} = \frac{3}{6} = \frac{1}{2}$
$\frac{b_1}{b_2} = \frac{-5}{-10} = \frac{1}{2}$
$\frac{c_1}{c_2} = \frac{-20}{-40} = \frac{1}{2}$
Since $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$,the lines are coincident.
Therefore,the system of linear equations has infinitely many solutions.