To determine which pairs of equations have exactly the same solution, we need to solve each equation or pair of equations.
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First pair: \( \frac{3}{8}x = 1 \) and \( \frac{1}{3}x = \frac{1}{8} \)
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Solve \( \frac{3}{8}x = 1 \): \[ x = 1 \cdot \frac{8}{3} = \frac{8}{3} \]
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Solve \( \frac{1}{3}x = \frac{1}{8} \): \[ x = \frac{1}{8} \cdot 3 = \frac{3}{8} \]
These equations do not have the same solution.
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Second pair: \( -3.2x = 0.64 \) and \( \frac{x}{4} = -0.05 \)
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Solve \( -3.2x = 0.64 \): \[ x = \frac{0.64}{-3.2} = -0.2 \]
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Solve \( \frac{x}{4} = -0.05 \): \[ x = -0.05 \cdot 4 = -0.2 \]
These equations have the same solution: \( x = -0.2 \).
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Third pair: \( -\frac{3}{4}x = 5 \) and \( 2x = -\frac{3}{4} \)
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Solve \( -\frac{3}{4}x = 5 \): \[ x = 5 \cdot -\frac{4}{3} = -\frac{20}{3} \]
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Solve \( 2x = -\frac{3}{4} \): \[ x = -\frac{3}{4} \cdot \frac{1}{2} = -\frac{3}{8} \]
These equations do not have the same solution.
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Fourth pair: \( \frac{x}{3.2} = 1.8 \) and \( 1.8x = 3.2 \)
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Solve \( \frac{x}{3.2} = 1.8 \): \[ x = 1.8 \cdot 3.2 = 5.76 \]
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Solve \( 1.8x = 3.2 \): \[ x = \frac{3.2}{1.8} = \frac{32}{18} = \frac{16}{9} \approx 1.7777 \]
These equations do not have the same solution.
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Based on the analysis, the only pair of equations that has exactly the same solution is the second pair:
\( -3.2x = 0.64 \) and \( \frac{x}{4} = -0.05 \).
1 answer