A box containing a total of 179 copies of two different paperback books was shipped to Marci’s school. The total weight of the books was 128 pounds. If the weight of each of the first paperbacks was two-thirds of a pound and the weight of each of the second paperbacks was three-fourths of a pound, which statements are true? Check all that apply.

- The system of equations is \( x + y = 179 \) and \( \frac{2}{3}x + \frac{3}{4}y = 128 \).

- The system of equations is \( x + y = 128 \) and \( \frac{2}{3}x + \frac{3}{4}y = 179 \).

- To eliminate the x-variable from the equations, you can multiply the equation with the fractions by 3 and leave the other equation as it is.

- To eliminate the y-variable from the equations, you can multiply the equation with the fractions by –4 and multiply the other equation by 3.

- There are 104 copies of one book and 24 copies of the other.

The first statement correctly represents the system of equations that can be used to solve the problem. x represents the number of copies of the first paperback book, y represents the number of copies of the second paperback book, and the equations reflect the total number of copies and their respective weights.

To eliminate the x-variable from the equations, you can multiply the equation with the fractions by 3 and leave the other equation as it is.

This statement is true. To eliminate the x-variable, you can multiply the equation Two-thirds x + three-fourths y = 128 by 3, which results in 2x + (9/4)y = 384.

To eliminate the y-variable from the equations, you can multiply the equation with the fractions by –4 and multiply the other equation by 3.

This statement is also true. To eliminate the y-variable, you can multiply the equation Two-thirds x + three-fourths y = 128 by -4, which gives you (-8/3)x - 3y = -512. Multiplying the equation x + y = 179 by 3 gives you 3x + 3y = 537.

The statement "There are 104 copies of one book and 24 copies of the other" is not necessarily true. The solution to the system of equations will provide the values of x and y, which represent the number of copies of each book. Without solving the equations, we cannot determine the specific quantities.

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