To determine which pairs of equations have exactly the same solution, let's solve each pair of equations one by one.
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Equation Pair: -3.2x = 0.64 and x/4 = -0.05
For the first equation: \[ -3.2x = 0.64 \implies x = \frac{0.64}{-3.2} = -0.2 \]
For the second equation: \[ \frac{x}{4} = -0.05 \implies x = -0.05 \times 4 = -0.2 \]
Both equations have the solution \(x = -0.2\).
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Equation Pair: -3/4x = 5/2 and 5/2x = -3/4
For the first equation: \[ -\frac{3}{4}x = \frac{5}{2} \implies x = \frac{\frac{5}{2}}{-\frac{3}{4}} = \frac{5}{2} \times -\frac{4}{3} = -\frac{10}{3} \]
For the second equation: \[ \frac{5}{2}x = -\frac{3}{4} \implies x = \frac{-\frac{3}{4}}{\frac{5}{2}} = -\frac{3}{4} \times \frac{2}{5} = -\frac{3}{10} \]
These equations do not have the same solution.
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Equation Pair: 3/8x = 1 and 1/3x = 1/8
For the first equation: \[ \frac{3}{8}x = 1 \implies x = 1 \times \frac{8}{3} = \frac{8}{3} \]
For the second equation: \[ \frac{1}{3}x = \frac{1}{8} \implies x = \frac{1}{8} \times 3 = \frac{3}{8} \]
These equations do not have the same solution.
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Equation Pair: x/3.2 = 1.8 and 1.8x = 3.2
For the first equation: \[ \frac{x}{3.2} = 1.8 \implies x = 1.8 \times 3.2 = 5.76 \]
For the second equation: \[ 1.8x = 3.2 \implies x = \frac{3.2}{1.8} = \frac{32}{18} \implies x = \frac{16}{9} \approx 1.78 \]
These equations do not have the same solution.
Conclusion
The only pair of equations with exactly the same solution is the first pair:
-3.2x = 0.64 and x/4 = -0.05, both yielding \(x = -0.2\).
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