Question

Which of the following equations have infinitely many solutions? Choose all answers that apply: a. 57x + 57 = −75x − 7557x + 57 = −75x − 75 b. −75x + 57 = −75x + 57 − 75x + 57 = −75x + 57 c. 75x + 57 = −75x + 5775x + 57 = −75x + 5 d. −57x + 57 = −75x + 75

Answer 1

The equations that have infinitely many solutions are a. 57x + 57 = -75x - 75 and b. -75x + 57 = -75x + 57.

Step-by-step 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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