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Answer :
The statements that are true are:
The system of equations is x + y = 179 and Two-thirds x + three-fourths y = 128.
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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