Answer: To graph this system of inequalities, we can first graph each inequality separately and then find the region where they overlap.
Starting with the first inequality, x - y ≥ 7, we can rearrange it to y ≤ x - 7 and graph the line y = x - 7. Since the inequality includes the line, we will use a solid line to represent it, and shade below the line to show the region where y is less than or equal to x - 7.
Next, for the second inequality, x + 2y < 5, we can rearrange it to y < (-1/2)x + 5/2 and graph the line y = (-1/2)x + 5/2. Since the inequality excludes the line, we will use a dashed line to represent it, and shade below the line to show the region where y is less than (-1/2)x + 5/2.
Now we can combine the two shaded regions to find the overlapping region where both inequalities are satisfied. This region is shown in the graph below:
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The point that represents a solution to the system is the point where the two lines intersect. To find this point, we can solve the system of equations:
y = x - 7
y = (-1/2)x + 5/2
Substituting the first equation into the second, we get:
x - 7 = (-1/2)x + 5/2
Simplifying this equation, we get:
(3/2)x = 19/2
x = 19/3
Substituting this value of x into either of the original equations, we get:
y = 19/3 - 7 = 2/3
So the point that represents a solution to the system is (19/3, 2/3).
Explanation: