How many nonnegative integer solutions exist for x1 + x2 = 5?

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Multiple Choice

How many nonnegative integer solutions exist for x1 + x2 = 5?

Explanation:
This uses the idea that for a fixed sum with two nonnegative integers, the first variable can take any value from 0 up to that sum, and the second is determined as the remainder. Here, x1 can be 0, 1, 2, 3, 4, or 5, giving six possibilities. The corresponding pairs are (0,5), (1,4), (2,3), (3,2), (4,1), and (5,0). So there are six nonnegative integer solutions in total.

This uses the idea that for a fixed sum with two nonnegative integers, the first variable can take any value from 0 up to that sum, and the second is determined as the remainder. Here, x1 can be 0, 1, 2, 3, 4, or 5, giving six possibilities. The corresponding pairs are (0,5), (1,4), (2,3), (3,2), (4,1), and (5,0). So there are six nonnegative integer solutions in total.

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