Which one of the following pairs of linear equations has/ have infinite many solutions?

(A) $9x + 3y + 12 = 0$, and $18x + 6y + 24 = 0$

(B) $2x - 3y = 13$, and $7x - 2y = 20$

(C) $x + y = 5$, $2x + 2y = 10$

(D) $3x + y - 3 = 0$ and $2x + \frac{2}{3}y = 2$

Choose the correct answer from the options given below:

Two linear equations have infinitely many solutions when they represent the same line. This occurs when one equation is a multiple of the other.

For equations $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$, they have infinitely many solutions when:

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

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(A) $9x + 3y + 12 = 0$ and $18x + 6y + 24 = 0$

$\frac{9}{18} = \frac{1}{2}$

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

$\frac{12}{24} = \frac{1}{2}$

All ratios are equal. This pair has infinitely many solutions.

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(B) $2x - 3y - 13 = 0$ and $7x - 2y - 20 = 0$

$\frac{2}{7} = \frac{2}{7}$

$\frac{-3}{-2} = \frac{3}{2}$

The ratios are not equal. This pair has a unique solution only.

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(C) $x + y - 5 = 0$ and $2x + 2y - 10 = 0$

$\frac{1}{2} = \frac{1}{2}$

$\frac{1}{2} = \frac{1}{2}$

$\frac{-5}{-10} = \frac{1}{2}$

All ratios are equal. This pair has infinitely many solutions.

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(D) $3x + y - 3 = 0$ and $2x + \frac{2}{3}y - 2 = 0$

$\frac{3}{2} = \frac{3}{2}$

$\frac{1}{\frac{2}{3}} = 1 \times \frac{3}{2} = \frac{3}{2}$

$\frac{-3}{-2} = \frac{3}{2}$

All ratios are equal. This pair has infinitely many solutions.

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The pairs with infinitely many solutions are (A), (C), and (D).

Therefore, the correct answer is: (A), (C), and (D) only.