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 determine which pairs of equations have exactly the same solution, we can simplify each equation and compare the simplified forms.
A. x/3.2 = 1.8 and 1.8x = 3.2
In the first equation, we can multiply both sides by 3.2 to eliminate the denominator:
x = 5.76
In the second equation, we can divide both sides by 1.8 to solve for x:
x = 1.778
The solutions are not exactly the same, so 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 eliminate the fraction:
x = 8/3
In the second equation, we can multiply both sides by 3/8 to solve for x:
x = 3/8
The solutions are not exactly the same, so 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 solve for x:
x = -0.2
In the second equation, we can multiply both sides by 4 to eliminate the fraction:
x = -0.2
The solutions are exactly the same, so 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 eliminate the fraction:
x = -10/3
In the second equation, we can multiply both sides by 2/5 to solve for x:
x = -10/3
The solutions are exactly the same, so this pair of equations has the same solution.
Therefore, the pairs of equations with exactly the same solution are C (-3.2x = 0.64 and x/4 = -0.05) and D (-3/4x = 5/2 and 5/2x = -3/4).