Which of the following pairs of equations has exactly the same solution?
A. x/3.2 = 1.8 and 1.8x = 3.2
B. 3/8x = 1 and 1/3x = 1/8
C. -3.2x = 0.64 and x/4 = -0.05
D. -3/4x = 5/2 and 5/2x = -3/4
To find out which pair of equations has exactly the same solution, we need to solve each pair of equations and check if they have the same solution.
A. x/3.2 = 1.8 and 1.8x = 3.2
In the first equation, we can multiply both sides by 3.2 to isolate x:
x = 1.8 * 3.2 = 5.76
Now, let's solve the second equation:
1.8x = 3.2
Divide both sides by 1.8:
x = 3.2/1.8 ≈ 1.78
The solution to the first equation is approximately 5.76, while the solution to the second equation is approximately 1.78. Therefore, this pair of equations does not have the same solution.
B. 3/8x = 1 and 1/3x = 1/8
In the first equation, we can multiply both sides by 8/3 to isolate x:
x = (8/3) * 1 = 8/3
Now, let's solve the second equation:
(1/3)x = 1/8
Multiply both sides by 24 to get rid of the fractions:
8x = 3
Divide both sides by 8:
x = 3/8
The solution to the first equation is 8/3, while the solution to the second equation is 3/8. Therefore, this pair of equations does not have the same solution.
C. -3.2x = 0.64 and x/4 = -0.05
In the first equation, we can divide both sides by -3.2 to isolate x:
x = 0.64/-3.2 = -0.2
Now, let's solve the second equation:
x/4 = -0.05
Multiply both sides by 4 to isolate x:
x = -0.05 * 4 = -0.2
The solution to the first equation is -0.2, while the solution to the second equation is -0.2. Therefore, this pair of equations has the same solution.
D. -3/4x = 5/2 and 5/2x = -3/4
In the first equation, we can multiply both sides by 4/(-3) to isolate x:
x = (4/(-3)) * (5/2) = -10/6 = -5/3
Now, let's solve the second equation:
(5/2)x = -3/4
Multiply both sides by 2/5 to isolate x:
x = (-3/4) * (2/5) = -6/20 = -3/10
The solution to the first equation is -5/3, while the solution to the second equation is -3/10. Therefore, this pair of equations does not have the same solution.
Therefore, the correct pair of equations that has exactly the same solution is C. -3.2x = 0.64 and x/4 = -0.05.