Which of the following pair of linear equations is inconsistent?

(A) x - y = 5; 3x - 3y = 10

(B) 2x + 3y = 4; 4x + 6y = 8

(C) 9x + 6y = 6; 3x + 2y = 3

(D) 2x + 5y = 2; 6x - 15y = 4

Choose the correct answer from the options given below:

An inconsistent system of linear equations has no solution - the two lines are parallel and never meet.

For two equations: $a_1x + b_1y = c_1$ and $a_2x + b_2y = c_2$

The system is inconsistent when:

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

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(A) $x - y = 5$; $3x - 3y = 10$

$\frac{a_1}{a_2} = \frac{1}{3}$

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

$\frac{c_1}{c_2} = \frac{5}{10} = \frac{1}{2}$

Since $\frac{1}{3} = \frac{1}{3} \neq \frac{1}{2}$, this system is inconsistent.

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(B) $2x + 3y = 4$; $4x + 6y = 8$

$\frac{a_1}{a_2} = \frac{2}{4} = \frac{1}{2}$

$\frac{b_1}{b_2} = \frac{3}{6} = \frac{1}{2}$

$\frac{c_1}{c_2} = \frac{4}{8} = \frac{1}{2}$

Since $\frac{1}{2} = \frac{1}{2} = \frac{1}{2}$, this system has infinite solutions (same line).

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(C) $9x + 6y = 6$; $3x + 2y = 3$

$\frac{a_1}{a_2} = \frac{9}{3} = 3$

$\frac{b_1}{b_2} = \frac{6}{2} = 3$

$\frac{c_1}{c_2} = \frac{6}{3} = 2$

Since $3 = 3 \neq 2$, this system is inconsistent.

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(D) $2x + 5y = 2$; $6x - 15y = 4$

$\frac{a_1}{a_2} = \frac{2}{6} = \frac{1}{3}$

$\frac{b_1}{b_2} = \frac{5}{-15} = -\frac{1}{3}$

Since $\frac{1}{3} \neq -\frac{1}{3}$, this system has a unique solution.

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Both (A) and (C) are inconsistent pairs of linear equations.