To determine which of the options shows a system of equations equivalent to \(2x + 7y = 14\) and \(4x + 5y = 10\), we need to check if the alternative equations can be derived from these original equations.
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For \(2x + 7y = 14\): If we multiply this equation by 2, we get: \[ 2(2x + 7y) = 2(14) \Rightarrow 4x + 14y = 28 \]
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For \(4x + 5y = 10\): If we multiply this equation by 2, we get: \[ 2(4x + 5y) = 2(10) \Rightarrow 8x + 10y = 20 \]
Thus, the equivalent system from the original equations can be found as: \[ 4x + 14y = 28 \quad \text{and} \quad 8x + 10y = 20 \]
Hence, the correct answer is: 4x + 14y = 28 and 8x + 10y = 20.