To determine which of the options can use both intercepts to produce viable solutions, we should consider the nature of the variables involved and the relationships typically present between them.
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(years of experience, starting salary) - This relationship is often linear, where increased years of experience usually correlate to a higher starting salary. Both intercepts can provide meaningful insights here; the y-intercept could represent a baseline salary without experience, and the x-intercept could indicate where salary approaches zero, which may reveal a threshold of experience needed to receive a salary.
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(temperature, number of car rentals) - This can be a non-linear relationship, possibly influenced by various external factors. It may not have a clear intercept significance because temperatures (especially extreme ones) may not directly correlate to the number of car rentals in a straightforward manner.
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(age, weight) - The relationship between age and weight does not typically present a clear linear pattern, especially since it can vary significantly across different life stages and among individuals. Thus, using intercepts here may not yield meaningful solutions.
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(number of nominations, number of awards) - There is likely a positive correlation between nominations and awards, but potentially not a linear one. The x-intercept may not hold relevant real-world meaning (e.g., if someone has zero nominations, they would likely have zero awards), making the use of intercepts suspect in terms of viability.
Considering these points, the first option, (years of experience, starting salary), is the one that clearly can use both intercepts effectively to analyze the relationship and yield viable solutions.