To determine the truth about the equation \(3y - 1 = 13 - 4y\), we can solve it step by step.
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Start with the original equation: \[ 3y - 1 = 13 - 4y \]
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Add \(4y\) to both sides: \[ 3y + 4y - 1 = 13 \] \[ 7y - 1 = 13 \]
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Add \(1\) to both sides: \[ 7y = 13 + 1 \] \[ 7y = 14 \]
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Now, divide both sides by \(7\): \[ y = \frac{14}{7} = 2 \]
Since we found a single value \(y = 2\) that satisfies the equation, we can conclude that the equation has one solution.
Thus, the correct statement is: The equation has one solution.