Question

Which of the following pairs of equations has exactly the same solution?(1 point)
Responses

38x=1
and 13x=18
Start Fraction 3 over 8 End Fraction x equals 1 and Start Fraction 1 over 3 End Fraction x equals Start Fraction 1 over 8 End Fraction

−3.2x=0.64
and x4=−0.05
negative 3.2x equals 0.64 and Start Fraction x over 4 End Fraction equals negative 0.05

−34x=52
and 52x=−34
negative Start Fraction 3 over 4 End Fraction x equals Start Fraction 5 over 2 End Fraction and Start Fraction 5 over 2 End Fraction x equals negative Start Fraction 3 over 4 End Fraction

x3.2=1.8
and 1.8x=3.2

Answer 1

To determine which of the given pairs of equations has exactly the same solution, we need to simplify each pair and check if they yield the same result.

1. **First pair:**
- \(38x = 1\)
- \(13x = 18\)

Solve for \(x\):
- \(x = \frac{1}{38}\)
- \(x = \frac{18}{13}\)

These are not equal, so this pair does not have the same solution.

2. **Second pair:**
- \(\frac{3}{8}x = 1\)
- \(\frac{1}{3}x = \frac{1}{8}\)

Solve for \(x\):
- \(x = \frac{8}{3}\)
- Multiplying both sides of \(\frac{1}{3}x = \frac{1}{8}\) by 3 gives \(x = \frac{3}{8}\).

These are not equal, so this pair does not have the same solution.

3. **Third pair:**
- \(-3.2x = 0.64\)
- \(x/4 = -0.05\)

Solve for \(x\):
- \(x = \frac{0.64}{-3.2} = -0.2\)
- \(x = -0.05 \cdot 4 = -0.2\)

These are equal, so this pair has the same solution.

4. **Fourth pair:**
- \(-\frac{3}{4}x = \frac{5}{2}\)
- \(\frac{5}{2}x = -\frac{3}{4}\)

Solve for \(x\):
- \(x = -\frac{5}{2} \cdot \left(-\frac{4}{3}\right) = \frac{10}{3}\)
- \(x = -\frac{3}{4} \cdot \left(\frac{2}{5}\right) = -\frac{3}{10}\)

These are not equal, so this pair does not have the same solution.

5. **Fifth pair:**
- \(x \cdot 3.2 = 1.8\)
- \(1.8x = 3.2\)

Solve for \(x\):
- \(x = \frac{1.8}{3.2}\)
- \(x = \frac{3.2}{1.8}\)

These are not equal, so this pair does not have the same solution.

### Conclusion:
The pair of equations that has exactly the same solution is:
**−3.2x = 0.64 and x/4 = −0.05**