Final answer:
After adding the system of equations 2.5y + 3x = 27 and 5x – 2.5y = 5 correctly, the result is the equation 8x = 32, which simplifies to x = 4. However, this correct answer does not match any of the provided options, suggesting a possible error in the question or the answer choices.
Step-by-step explanation:
To solve the system of equations: 2.5y + 3x = 27, 5x – 2.5y = 5, we need to find the result of adding the two equations together. Adding the equations, we combine like terms, so 3x added to 5x equals 8x, and 2.5y minus 2.5y cancels out, giving us 0y. We also combine the constants 27 and 5, for a total of 32. So, the equation resulting from adding these two equations is 8x + 0y = 32, which simplifies to 8x = 32. There seems to be a discrepancy because none of the answer choices provided matches with this correct answer. However, if we divide both sides of the correct equation by the coefficient of x, which is 8, we get x = 4. This corrected result is not reflected in the provided options and would need to be addressed.