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The graph shows two lines representing the equations y = 2x + 5 and x + y = 1.
Which ordered pair is in the solution set for the system of inequalities y ≥ 2x + 5 and x + y ≤ 1?
(-5,0)
(0,7)
(5,0)
(0,-7)
To find the solution set for the system of inequalities, we need to determine which ordered pairs satisfy both inequalities.
For the first inequality y ≥ 2x + 5, any point that lies on or above the line y = 2x + 5 will satisfy the inequality. Looking at the graph, we can see that the line y = 2x + 5 is a straight line with a positive slope, and it intersects the y-axis at (0, 5). Therefore, any point that lies on or above this line will satisfy the inequality.
For the second inequality x + y ≤ 1, any point that lies on or below the line x + y = 1 will satisfy the inequality. Looking at the graph, we can see that the line x + y = 1 is a straight line with a negative slope, and it intersects the x-axis at (1, 0). Therefore, any point that lies on or below this line will satisfy the inequality.
Now let's consider the given ordered pairs:
- (7, 0): This point does not lie on or above the line y = 2x + 5 and does not lie on or below the line x + y = 1. Therefore, it does not satisfy either inequality.
- (0, 7): This point lies on or above the line y = 2x + 5 and does not lie on or below the line x + y = 1. Therefore, it satisfies the inequality y ≥ 2x + 5 but does not satisfy the inequality x + y ≤ 1.
- (5, 0): This point lies on or above the line y = 2x + 5 and lies on or below the line x + y = 1. Therefore, it satisfies both inequalities and is in the solution set for the system of inequalities.
- (0, -7): This point does not lie on or above the line y = 2x + 5 and does not lie on or below the line x + y = 1. Therefore, it does not satisfy either inequality.
Therefore, the ordered pair (5, 0) is in the solution set for the system of inequalities y ≥ 2x + 5 and x + y ≤ 1.