Question

Which o the following pairs of equation has exactly the same solution?

3/8x = 1 and 1/3x = 1/8

-3.2x = 0.64 and z/4 = 0.05

z/3.2 = 1.8 and 1.8x = 3.2

-3/4x = 5/4 and 5/2x = -3/4

Answer 1

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:**
1. \( \frac{3}{8}x = 1 \)
\[ x = 1 \cdot \frac{8}{3} = \frac{8}{3} \]

2. \( \frac{1}{3}x = \frac{1}{8} \)
\[ x = \frac{1}{8} \cdot 3 = \frac{3}{8} \]

**Solutions:**
- First equation: \( x = \frac{8}{3} \)
- Second equation: \( x = \frac{3}{8} \)
- **Not the same solution.**

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**Pair 2:**
1. \( -3.2x = 0.64 \)
\[ x = \frac{0.64}{-3.2} = -0.2 \]

2. \( \frac{z}{4} = 0.05 \)
\[ z = 0.05 \cdot 4 = 0.2 \]

**Solutions:**
- First equation: \( x = -0.2 \)
- Second equation: \( z = 0.2 \)
- **Not the same solution.**

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**Pair 3:**
1. \( \frac{z}{3.2} = 1.8 \)
\[ z = 1.8 \cdot 3.2 = 5.76 \]

2. \( 1.8x = 3.2 \)
\[ x = \frac{3.2}{1.8} \approx 1.78 \]

**Solutions:**
- First equation: \( z = 5.76 \)
- Second equation: \( x \approx 1.78 \)
- **Not the same solution.**

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**Pair 4:**
1. \( -\frac{3}{4}x = \frac{5}{4} \)
\[ x = \frac{5}{4} \cdot -\frac{4}{3} = -\frac{5}{3} \]

2. \( \frac{5}{2}x = -\frac{3}{4} \)
\[ x = -\frac{3}{4} \cdot \frac{2}{5} = -\frac{3}{10} \]

**Solutions:**
- First equation: \( x = -\frac{5}{3} \)
- Second equation: \( x = -\frac{3}{10} \)
- **Not the same solution.**

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None of the pairs have the same solution.