To determine which pairs of equations have exactly the same solution, we can solve each equation in the pairs and compare their solutions.
Pair 1:
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\( \frac{3}{8}x = 1 \) \[ x = 1 \cdot \frac{8}{3} = \frac{8}{3} \]
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\( \frac{1}{3}x = \frac{1}{8} \) \[ x = \frac{1}{8} \cdot 3 = \frac{3}{8} \]
Solutions:
- First equation: \( x = \frac{8}{3} \)
- Second equation: \( x = \frac{3}{8} \)
- Not the same solution.
Pair 2:
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\( -3.2x = 0.64 \) \[ x = \frac{0.64}{-3.2} = -0.2 \]
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\( \frac{z}{4} = 0.05 \) \[ z = 0.05 \cdot 4 = 0.2 \]
Solutions:
- First equation: \( x = -0.2 \)
- Second equation: \( z = 0.2 \)
- Not the same solution.
Pair 3:
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\( \frac{z}{3.2} = 1.8 \) \[ z = 1.8 \cdot 3.2 = 5.76 \]
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\( 1.8x = 3.2 \) \[ x = \frac{3.2}{1.8} \approx 1.78 \]
Solutions:
- First equation: \( z = 5.76 \)
- Second equation: \( x \approx 1.78 \)
- Not the same solution.
Pair 4:
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\( -\frac{3}{4}x = \frac{5}{4} \) \[ x = \frac{5}{4} \cdot -\frac{4}{3} = -\frac{5}{3} \]
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\( \frac{5}{2}x = -\frac{3}{4} \) \[ x = -\frac{3}{4} \cdot \frac{2}{5} = -\frac{3}{10} \]
Solutions:
- First equation: \( x = -\frac{5}{3} \)
- Second equation: \( x = -\frac{3}{10} \)
- Not the same solution.
None of the pairs have the same solution.