Final answer:
After correctly adding the two given equations to eliminate the y variable and simplifying, we find that x² equals 81. Taking the square root of both sides, we determine that x equals ±9. Considering a positive value of x, the answer is x = 9.
Step-by-step explanation:
To solve for x when given the equations 2x² + 8y = 121.5 and x² - 8y = 121.5, we can subtract the second equation from the first to eliminate the y variable. Doing so gives us:
2x² + 8y - (x² - 8y) = 121.5 - 121.5
Which simplifies to:
x² = 0
Therefore, taking the square root of both sides gives us:
x = 0
However, since 0 is not an option in the provided choices and the subtraction of the equations looks to have been a mistake, let's add them instead:
2x² + 8y + (x² - 8y) = 121.5 + 121.5
Which simplifies to:
3x² = 243
Dividing both sides by 3, we get:
x² = 81
Finally, taking the square root of both sides gives us:
x = ± 9
Since we are looking for a positive value of x, the answer is x = 9.