Which of the following pairs of equations has exactly the same solution?
-3/4x = 5/2 and 5/2x = -3/4
-3.2x = 0.64 and x/4 = -0.05
3/8x = 1 and 1/3x = 1/8
x/3.2 = 1.8 and 1.8x = 3.2
To determine which pairs of equations have exactly the same solution, we need to solve each pair of equations and compare the solutions.
1) -3/4x = 5/2 and 5/2x = -3/4:
Solving the first equation:
-3/4x = 5/2
Multiplying both sides by -4/3 gives:
x = -20/6 = -10/3
Solving the second equation:
5/2x = -3/4
Multiplying both sides by 2/5 gives:
x = -6/20 = -3/10
The solutions to the first pair of equations are x = -10/3 and x = -3/10. Since these solutions are not the same, this pair of equations does not have exactly the same solution.
2) -3.2x = 0.64 and x/4 = -0.05:
Solving the first equation:
-3.2x = 0.64
Dividing both sides by -3.2 gives:
x = 0.64/(-3.2) = -0.2
Solving the second equation:
x/4 = -0.05
Multiplying both sides by 4 gives:
x = -0.05(4) = -0.2
The solutions to the second pair of equations are x = -0.2 and x = -0.2. Since these solutions are the same, this pair of equations has exactly the same solution.
3) 3/8x = 1 and 1/3x = 1/8:
Solving the first equation:
3/8x = 1
Multiplying both sides by 8/3 gives:
x = 8/3
Solving the second equation:
1/3x = 1/8
Multiplying both sides by 3 gives:
x = 3(1/8) = 3/8
The solutions to the third pair of equations are x = 8/3 and x = 3/8. Since these solutions are not the same, this pair of equations does not have exactly the same solution.
4) x/3.2 = 1.8 and 1.8x = 3.2:
Solving the first equation:
x/3.2 = 1.8
Multiplying both sides by 3.2 gives:
x = 3.2(1.8) = 5.76
Solving the second equation:
1.8x = 3.2
Dividing both sides by 1.8 gives:
x = 3.2/1.8 = 1.777...
The solutions to the fourth pair of equations are x = 5.76 and x = 1.777... Since these solutions are not exactly the same (although approximately close), this pair of equations does not have exactly the same solution.
Therefore, the pair of equations that has exactly the same solution is -3.2x = 0.64 and x/4 = -0.05.