Question

Two inequalities are shown: y>4x -6 and yπ≤ -5/2x-2. Which coordinate is a solution to the inequality? Select all that apply.

A) (1, 0)
B) (2, 3)
C) (-3, 4)
D) (0, -2)
E) (5, 1)

Answer 1

By testing each coordinate in both inequalities, it is found that the only point satisfying both inequalities is coordinate D (0, -2).

Step-by-step explanation:

To solve the inequalities y > 4x - 6 and y ≤ -\(5/2\)x - 2, we substitute the x and y values from each coordinate into both inequalities to determine if they make the inequality true.

1. For coordinate A (1, 0), we test:
   
   • Is 0 > 4(1) - 6? No, because 0 is not greater than -2.
   • Is 0 ≤ -\(5/2\)(1) - 2? Yes, because 0 is less than -\(7/2\).
2. For coordinate B (2, 3), we test:
   
   • Is 3 > 4(2) - 6? Yes, because 3 is greater than 2.
   • Is 3 ≤ -\(5/2\)(2) - 2? No, because 3 is not less than or equal to -7.
3. For coordinate C (-3, 4), we test:
   
   • Is 4 > 4(-3) - 6? No, because 4 is not greater than -18.
   • Is 4 ≤ -\(5/2\)(-3) - 2? Yes, because 4 is less than 7.5.
4. For coordinate D (0, -2), we test:
   
   • Is -2 > 4(0) - 6? Yes, because -2 is greater than -6.
   • Is -2 ≤ -\(5/2\)(0) - 2? Yes, because -2 is equal to -2.
5. For coordinate E (5, 1), we test:
   
   • Is 1 > 4(5) - 6? No, because 1 is not greater than 14.
   • Is 1 ≤ -\(5/2\)(5) - 2? No, because 1 is not less than or equal to -\(27/2\).

After testing all points, we find that the only coordinate that satisfies both inequalities is D (0, -2).