Final answer:
After evaluating each coordinate pair with the inequality y > |x| - 5, the pair (-4,1) is the only one that satisfies the condition, making it the correct answer.
Step-by-step explanation:
The question "Which of the following is a solution of y > |x| - 5?" is asking us to determine which coordinate pair satisfies the inequality. To find the solution, we plug in the x-value from each coordinate pair into the equation and check if the corresponding y-value is greater than the absolute value of the x-value minus 5.
- For option A (-4,1), we have: 1 > |-4| - 5, which simplifies to 1 > 4 - 5 which is 1 > -1. This is true.
- For option B (-1,-4), we have: -4 > |-1| - 5, which simplifies to -4 > 1 - 5 which is -4 > -4. This is not true because -4 is not greater than -4.
- For option C (4,-1), we have: -1 > |4| - 5, which simplifies to -1 > 4 - 5 which is -1 > -1. This is not true as -1 is not greater than -1.
Therefore, the correct answer is option A (-4,1), since it is the only pair that satisfies the inequality.