To determine the best approximation of the exact solution for Grace's system of equations based on the information provided, we need to analyze the constraints on the x-value. Grace narrowed down the potential range for the x-value to between 0.5 and 1.
Let's review the answer choices given:
- (0.5, 1.2) - Here, the x-value is 0.5.
- (0.6, 0.7) - Here, the x-value is 0.6.
- (0.7, 0.2) - Here, the x-value is 0.7.
- (0.9, 1.0) - Here, the x-value is 0.9.
Since the x-value must lie between 0.5 and 1, all of the choices are valid regarding x's range. However, the next step is to inspect the y-values.
If Grace is looking for an ordered pair that best approximates the exact solution, it generally implies that we want to choose the (x, y) pair that represents a point where both equations in the system would come close to intersecting.
Without specific details about the actual equations or results from her tables, I can infer that (0.6, 0.7), (0.7, 0.2), and (0.9, 1.0) are more probable candidates for intersection if they appear as solutions from computations relative to typical behaviors of systems preparing to converge.
Among these, the value pair (0.6, 0.7) appears promising for any system where both y outputs are close in value, as it stands relatively more balanced compared to the y-values given in the other ordered pairs.
Thus, the best approximation of the exact solution based on the provided choices is:
(0.6, 0.7).