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Answer :
Final answer:
The equations that have infinitely many solutions are a. 57x + 57 = -75x - 75 and b. -75x + 57 = -75x + 57.
Explanation:
The equations that have infinitely many solutions are a. 57x + 57 = -75x - 75 and b. -75x + 57 = -75x + 57. To determine if an equation has infinitely many solutions, we need to check if the equation simplifies to 0 = 0. If it does, then it has infinitely many solutions.
Let's check the two equations:
- a. 57x + 57 = -75x - 75:
57x + 75x = -75 - 57
132x = -132
x = -1 - b. -75x + 57 = -75x + 57:
-75x + 75x = -75 + 57
0 = -18
As we can see, both equations do not simplify to 0 = 0, which means they do not have infinitely many solutions. Therefore, the correct answer is none of the given equations have infinitely many solutions.
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