Answer:
Explanation:
The ordered pair that makes both inequalities true is (2, 1).
To determine this, let's analyze the given inequalities and the shaded regions on the coordinate plane.
The first inequality, y < 3x – 1, represents a dashed line with a positive slope. It passes through the points (0, -1) and (1, 2). Since everything to the right of this line is shaded, any point on or to the right of this line will satisfy the inequality.
The second inequality, y > –x + 4, represents a solid line with a negative slope. It passes through the points (0, 4) and (4, 0). Since everything above this line is shaded, any point on or above this line will satisfy the inequality.
Now, let's examine the given ordered pairs:
(4, 0): This point lies on the second line but does not satisfy the first inequality, as y = 0 and 0 is not less than 3x – 1.
(1, 2): This point lies on both lines and satisfies both inequalities. For the first inequality, y = 2 and 2 is less than 3x – 1. For the second inequality, y = 2 and 2 is greater than –x + 4. Therefore, (1, 2) is a valid solution.
(0, 4): This point lies on both lines and satisfies both inequalities. For the first inequality, y = 4 and 4 is less than 3x – 1. For the second inequality, y = 4 and 4 is greater than –x + 4. Therefore, (0, 4) is a valid solution.
(2, 1): This point lies on both lines and satisfies both inequalities. For the first inequality, y = 1 and 1 is less than 3x – 1. For the second inequality, y = 1 and 1 is greater than –x + 4. Therefore, (2, 1) is a valid solution.
In summary, the ordered pairs that make both inequalities true are (1, 2), (0, 4), and (2, 1).
an AI ANSWER