Question

Which of the following pairs of equations has exactly the same solution?(1 point) Responses x/3.2 = 1.8 and 1.8x = 3.2 −3.2x = 0.64 and x/4 = −0.05
3/8x = 1 and 1/3x = 1/8 −3/4x=5/2 and 5/2x=−3/4

Answer 1

To determine which pairs of equations have exactly the same solution, we can solve each pair of equations.

1. **First pair of equations:**
- \( x/3.2 = 1.8 \)
- \( 1.8x = 3.2 \)

For the first equation:
\[
x = 1.8 \times 3.2 = 5.76
\]

For the second equation:
\[
x = \frac{3.2}{1.8} \approx 1.78
\]

**So the first pair does not have the same solution.**

---

2. **Second pair of equations:**
- \( -3.2x = 0.64 \)
- \( x/4 = -0.05 \)

For the first equation:
\[
x = \frac{0.64}{-3.2} = -0.2
\]

For the second equation:
\[
x = -0.05 \times 4 = -0.2
\]

**So the second pair has the same solution.**

---

3. **Third pair of equations:**
- \( \frac{3}{8}x = 1 \)
- \( \frac{1}{3}x = \frac{1}{8} \)

For the first equation:
\[
x = 1 \div \frac{3}{8} = \frac{8}{3}
\]

For the second equation:
\[
x = \frac{1}{8} \times 3 = \frac{3}{8}
\]

**So the third pair does not have the same solution.**

---

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

For the first equation:
\[
x = \frac{5/2}{-3/4} = \frac{5/2} \times \left(-\frac{4}{3}\right) = -\frac{10}{3}
\]

For the second equation:
\[
x = \frac{-3/4}{5/2} = -\frac{3/4} \times \left(\frac{2}{5}\right) = -\frac{3}{10}
\]

**So the fourth pair does not have the same solution.**

---

From the checks, the only pair of equations that has exactly the same solution is the **second pair:**
\[
-3.2x = 0.64 \text{ and } x/4 = -0.05
\]