Question

Terri graphed a system of linear inequalities. The absolute value function f passes through the points (-8, 3), (-5, 0), (0, 5) and function g passes through the points (-6, 8), (-2, 0), (2, 8). Select ALL of the ordered pairs that are part of the solution set for this system of linear inequalities. A (−1,5) B (2,−4) C (7,−1) D (4,6) E (5,2)

Answer 1

None of the provided ordered pairs are part of the solution set for this system of linear inequalities.

Step-by-step explanation:

To find the solution set for the system of linear inequalities represented by the functions f and g, we need to determine which of the given ordered pairs satisfy both inequalities. Let's analyze each ordered pair:

• For the ordered pair (−1,5), we can substitute the values into both functions. Taking f(x) = |x|, we have f(-1) = |-1| = 1 and for g(x) = 3x + 11, we have g(-1) = 3(-1) + 11 = 8. Since the values do not satisfy both inequalities, (−1,5) is not part of the solution set.
• For the ordered pair (2,−4), we find f(2) = |2| = 2 and g(2) = 3(2) + 11 = 17. Again, the values do not satisfy both inequalities, so (2,−4) is not in the solution set.
• For the ordered pair (7,−1), we find f(7) = |7| = 7 and g(7) = 3(7) + 11 = 32. Since the values do not satisfy both inequalities, (7,−1) is not part of the solution set.
• For the ordered pair (4,6), we find f(4) = |4| = 4 and g(4) = 3(4) + 11 = 23. Again, the values do not satisfy both inequalities, so (4,6) is not in the solution set.
• Lastly, for the ordered pair (5,2), we find f(5) = |5| = 5 and g(5) = 3(5) + 11 = 26. Since the values do not satisfy both inequalities, (5,2) is not part of the solution set.

Therefore, none of the provided ordered pairs are part of the solution set for this system of linear inequalities.