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

Question

Responses

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

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

38x=1
3
8
𝑥
=
1
and 13x=18
1
3
𝑥
=
1
8
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
−
3
4
𝑥
=
5
2
and 52x=−34,....

Answer 1

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

1. Pair 1:

   • Equation 1: \( -3.2x = 0.64 \)
     \( x = \frac{0.64}{-3.2} = -0.2 \)

   • Equation 2: \( \frac{x}{4} = -0.05 \)
     \( x = -0.05 \times 4 = -0.2 \)

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

2. Pair 2:

   • Equation 1: \( x \cdot 3.2 = 1.8 \)
     \( x = \frac{1.8}{3.2} = 0.5625 \)

   • Equation 2: \( 1.8x = 3.2 \)
     \( x = \frac{3.2}{1.8} = 1.7777... \)

   The solutions are different.

3. Pair 3:

   • Equation 1: \( \frac{3}{8}x = 1 \)
     \( x = \frac{1}{(3/8)} = \frac{8}{3} \approx 2.6667\)

   • Equation 2: \( \frac{1}{3}x = \frac{1}{8} \)
     \( x = \frac{1/8}{1/3} = \frac{3}{8} \)

   The solutions are different.

4. Pair 4:

   • Equation 1: \( -\frac{3}{4}x = 52 \)
     \( x = \frac{52}{-3/4} = -\frac{52 \cdot 4}{3} = -\frac{208}{3} \approx -69.3333\)

   • Equation 2: \( 52x = -34 \)
     \( x = -\frac{34}{52} = -\frac{17}{26} \approx -0.6538\)

   The solutions are different.

Based on the analysis, the pair of equations that has exactly the same solution is Pair 1:

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