Question

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

−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

x3.2=1.8 and 1.8x=3.2
Start Fraction x over 3.2 End Fraction equals 1.8 and 1.8x equals 3.2

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

−34x=52 and 52x=−34

Answer 1

To determine which of the given pairs of equations have exactly the same solution, we need to solve each equation within each pair.

1. \( -3.2x = 0.64 \) and \( \frac{x}{4} = -0.05 \)

Solving \( -3.2x = 0.64 \):
\[
x = \frac{0.64}{-3.2} = -0.2
\]

Solving \( \frac{x}{4} = -0.05 \):
\[
x = -0.05 \times 4 = -0.2
\]

Both equations have the same solution, \( x = -0.2 \).

2. \( \frac{x}{3.2} = 1.8 \) and \( 1.8x = 3.2 \)

Solving \( \frac{x}{3.2} = 1.8 \):
\[
x = 1.8 \times 3.2 = 5.76
\]

Solving \( 1.8x = 3.2 \):
\[
x = \frac{3.2}{1.8} \approx 1.778
\]

These equations do not have the same solution.

3. \( \frac{3}{8}x = 1 \) and \( \frac{1}{3}x = \frac{1}{8} \)

Solving \( \frac{3}{8}x = 1 \):
\[
x = \frac{1} {\frac{3}{8}} = \frac{8}{3}
\]

Solving \( \frac{1}{3}x = \frac{1}{8} \):
\[
x = \frac{1}{8} \times 3 = \frac{3}{8}
\]

These equations do not have the same solution.

4. \( -\frac{34}{x} = 52\) and \( 52x = -34 \)

Solving \( -\frac{34}{x} = 52 \):
\[
x = -\frac{34}{52} = -\frac{17}{26} = -\frac{17}{26}
\]

Solving \( 52x = -34 \):
\[
x = \frac{-34}{52} = -\frac{17}{26}
\]

Both equations have the same solution \( x = -\frac{17}{26} \).

Hence, the pairs of equations with exactly the same solution are:

- \( -3.2x = 0.64 \) and \( \frac{x}{4} = -0.05 \)
- \( -\frac{34}{x} = 52\) and \( 52x = -34 \)

So the correct response among provided options is:
- \(-3.2x = 0.64 \) and \( \frac{x}{4} = -0.05 \)