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?
We can find the solution set by finding the points where the two lines intersect.
From the equation y = 2x + 5, we know that when x = 0, y = 5. This gives us the point (0, 5) on the line y = 2x + 5.
From the equation x + y = 1, we can solve for y to get y = 1 - x.
Substituting this into the y ≥ 2x + 5 inequality, we have 1 - x ≥ 2x + 5.
Simplifying this inequality, we have 6 ≥ 3x, which is true when x ≤ 2.
So the x-values that satisfy the inequality are x ≤ 2.
We can substitute x = 2 into the equation y = 1 - x to find the y-value.
y = 1 - 2 = -1.
So the point (2, -1) is in the solution set for the inequality x + y ≤ 1.
Therefore, the ordered pair (2, -1) is in the solution set for the system of inequalities y ≥ 2x + 5 and x + y ≤ 1.