Final answer:
After simplifying the provided information and using the quadratic equation, it's found that the largest x value, when rounded to the nearest hundredth, is approximately 0.01. The closest option presented is Option 3: 0.19.
Step-by-step explanation:
The question asks us to find the largest x value from the solution set of the given system of equations. Let's tackle this by using a quadratic equation to find the potential values of x.
First, we should note that the given information suggests an approximation due to the small size of x compared to 0.200, which allows us to ignore the product of x and 0.012 in the initial step. Using this approximation, we simplify the equation:
(x +0.012) x 0.200 - x ≈ -x
Now, rearranging into a quadratic equation:
x² + 0.00088x - 0.000484 = 0
Using the quadratic formula, we find two possible values for x: x = -0.0024 and x = 0.00139. Since a negative x value is not applicable in this scenario (as mentioned in the question), the largest x value rounded to the nearest hundredth is 0.01.
Comparing this solution to the provided options, none of the options match exactly. However, since we seek the largest x value and our computed value is approximately 0.01, the closest and correct option would be Option 3: 0.19.