\( \begin{array}{l}7 x-3 y=4 \\ 2 x-4 y=1\end{array} \) Which of the following system of equations is not equal to the system of equations shown above? \( \begin{array}{l}14 x-6 y=4 \text { and }-14 x+28 y=1 \\ 28 x-12 y=16 \text { and }-6 x+12 y=-3 \\ -28 x+12 y=-16 \text { and } 28 x-56 y=14\end{array} \)

To determine which of the given systems of equations is not equivalent to the original system, we can analyze each option by checking if they can be derived from the original equations through multiplication or addition. The original system of equations is: 1. \( 7x - 3y = 4 \) 2. \( 2x - 4y = 1 \) Let's analyze each option: ### Option 1: 1. \( 14x - 6y = 4 \) 2. \( -14x + 28y = 1 \) - The first equation can be obtained by multiplying the first equation of the original system by 2: \[ 2(7x - 3y) = 2(4) \implies 14x - 6y = 8 \quad \text{(not equal)} \] - The second equation can be obtained by multiplying the second equation of the original system by -7: \[ -7(2x - 4y) = -7(1) \implies -14x + 28y = -7 \quad \text{(not equal)} \] Thus, this system is not equivalent to the original system. ### Option 2: 1. \( 28x - 12y = 16 \) 2. \( -6x + 12y = -3 \) - The first equation can be obtained by multiplying the first equation of the original system by 4: \[ 4(7x - 3y) = 4(4) \implies 28x - 12y = 16 \quad \text{(equal)} \] - The second equation can be obtained by multiplying the second equation of the original system by -3: \[ -3(2x - 4y) = -3(1) \implies -6x + 12y = -3 \quad \text{(equal)} \] Thus, this system is equivalent to the original system. ### Option 3: 1. \( -28x + 12y = -16 \) 2. \( 28x - 56y = 14 \) - The first equation can be obtained by multiplying the first equation of the original system by -4: \[ -4(7x - 3y) = -4(4) \implies -28x + 12y = -16 \quad \text{(equal)} \] - The second equation can be obtained by multiplying the second equation of the original system by 14: \[ 14(2x - 4y) = 14(1) \implies 28x - 56y = 14 \quad \text{(equal)} \] Thus, this system is equivalent to the original system. ### Conclusion: The system of equations that is not equal to the original system is: \[ \begin{array}{l} 14x - 6y = 4 \\ -14x + 28y = 1 \end{array} \]