To determine which pair of equations has exactly the same solution, we need to solve each pair of equations separately.
1) -3/4x + 5/2 and 5/2x = 3/4
Simplifying the first equation, we have:
-3/4x + 5/2 = 0
To solve for x, we can subtract 5/2 from both sides:
-3/4x = -5/2
Now, multiply both sides by -4/3 to isolate x:
x = (-5/2) * (-4/3)
x = 10/3
For the second equation, we have:
5/2x = 3/4
We can multiply both sides by 2/5:
x = (3/4) * (2/5)
x = 6/20
x = 3/10
The solutions for the first equation and the second equation are x = 10/3 and x = 3/10, respectively. These solutions are not the same.
2) x/3.2 = 1.8 and 1.8 = 3.2
For the first equation, we have:
x/3.2 = 1.8
To solve for x, we can multiply both sides by 3.2:
x = 3.2 * 1.8
x = 5.76
For the second equation, we have:
1.8 = 3.2
This equation states that 1.8 is equal to 3.2. However, this is not true, so this equation does not have a solution.
3) 3/8x = 1 and 1/3x = 1/8
For the first equation, we have:
3/8x = 1
To solve for x, we can multiply both sides by 8/3:
x = (1) * (8/3)
x = 8/3
For the second equation, we have:
1/3x = 1/8
To solve for x, we can multiply both sides by 8/1:
x = (1/8) * (8/1)
x = 1
The solutions for the first equation and the second equation are x = 8/3 and x = 1, respectively. These solutions are not the same.
4) -3.2 = .64 and x/4 = -.05
For the first equation, we have:
-3.2 = .64
This equation states that -3.2 is equal to 0.64. However, this is not true, so this equation does not have a solution.
For the second equation, we have:
x/4 = -0.05
To solve for x, we can multiply both sides by 4:
x = -0.05 * 4
x = -0.2
The solutions for the first equation and the second equation are not the same.
Therefore, none of the pairs of equations have the same solution.