Final answer:
Option C, 5.1 + 2y + 1.2 = -2 + 2y + 8.3, is the equation with infinitely many solutions, as upon simplifying both sides become identical, yielding the true statement 6.3 = 6.3 for any value of y.
Step-by-step explanation:
To determine which equation has infinitely many solutions, we need to look for an equation where, after simplification, both sides are identical, indicating that the equation is true for any value of the variable. Let's analyze each option step by step:
- A. -6.8+3y+2.4=4.3-3y: Combine like terms on each side and add 3y to both sides to get 3y - 3y + (-6.8 + 2.4) = 4.3 - 3y + 3y which simplifies to 0 = 4.3 - 4.4, or 0 = -0.1. This equation does not have infinitely many solutions, as the two sides are not equal.
- B. 0.5y + 2.5 - 0.66y + 1.2: This equation is incomplete and not provided in a standard format. We'll disregard this option since it's unclear.
- C. 5.1 + 2y + 1.2 = -2 + 2y + 8.3: Combine like terms on each side. On the left, we have 5.1 + 1.2 = 6.3, and on the right, -2 + 8.3 = 6.3. Subtract 2y from both sides to get 6.3 = 6.3. This shows that the equation is true for all values of y, indicating infinitely many solutions.
- D. 0.4y = 2.3 + 1.5y: Move the y terms to one side by subtracting 0.4y from both sides to get 0 = 2.3 + 1.1y. This does not represent an equation with infinitely many solutions, as the value of y must satisfy the equation, which is not the case for all values of y.
Based on our analysis, option C is the equation with infinitely many solutions, as simplifying it leads to a true statement regardless of the value of y.