High School

Which of the following equations have infinitely many solutions? Choose all answers that apply:

A. \( 57x + 57 = -75x - 75 \)

B. \( -75x + 57 = -75x + 57 \)

C. \( 75x + 57 = -75x + 5 \)

D. \( -57x + 57 = -75x + 75 \)

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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