To determine which pairs of equations have exactly the same solution, we can solve each pair of equations one by one.
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First Pair: \( -3.2x = 0.64 \) and \( \frac{x}{4} = -0.05 \)
Solving \( -3.2x = 0.64 \): \[ x = \frac{0.64}{-3.2} = -0.2 \]
Solving \( \frac{x}{4} = -0.05 \): \[ x = -0.05 \cdot 4 = -0.2 \]
Both equations yield the same solution: \( x = -0.2 \).
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Second Pair: \( \frac{x}{3.2} = 1.8 \) and \( 1.8x = 3.2 \)
Solving \( \frac{x}{3.2} = 1.8 \): \[ x = 1.8 \cdot 3.2 = 5.76 \]
Solving \( 1.8x = 3.2 \): \[ x = \frac{3.2}{1.8} = \frac{32}{18} = \frac{16}{9} \approx 1.78 (not the same as 5.76) \]
The solutions are not the same.
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Third Pair: \( \frac{3}{8}x = 1 \) and \( \frac{1}{3}x = \frac{1}{8} \)
Solving \( \frac{3}{8}x = 1 \): \[ x = 1 \cdot \frac{8}{3} = \frac{8}{3} \]
Solving \( \frac{1}{3}x = \frac{1}{8} \): \[ x = \frac{1}{8} \cdot 3 = \frac{3}{8} \]
The solutions are not the same.
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Fourth Pair: \( -\frac{3}{4}x = \frac{5}{2} \) and \( \frac{5}{2}x = -\frac{3}{4} \)
Solving \( -\frac{3}{4}x = \frac{5}{2} \): \[ x = \frac{5/2}{-3/4} = \frac{5}{2} \cdot \frac{-4}{3} = -\frac{10}{3} \]
Solving \( \frac{5}{2}x = -\frac{3}{4} \): \[ x = -\frac{3/4}{5/2} = -\frac{3}{4} \cdot \frac{2}{5} = -\frac{3}{10} \]
The solutions are not the same.
Summary of Results: The first pair of equations, \( -3.2x = 0.64 \) and \( \frac{x}{4} = -0.05 \), has the same solution \( x = -0.2 \). The other pairs do not have the same solution.
Final Answer: The first pair has exactly the same solution.