Answer: The shaded region would be below the solid line for 5x + y ≤ 1 and below the dashed line for y < 6.
Step-by-step explanation: To graph the system of linear inequalities, we will graph each inequality separately and then identify the region where the shaded areas overlap.
1) Graphing the inequality 5x + y ≤ 1:
To graph this inequality, we need to rewrite it in slope-intercept form (y = mx + b):
y ≤ -5x + 1
To graph this inequality, we start by plotting the y-intercept, which is 1. Then, using the slope, which is -5, we can find additional points to draw a line. Since the inequality includes "y ≤," we will draw a solid line to represent all the points on and below the line.
2) Graphing the inequality y < 6:
To graph this inequality, we draw a horizontal dashed line at y = 6. The inequality does not include "y =" but instead "y <," which means the line should be dashed to represent all the points below the line but not including the line itself.
After graphing both inequalities, we can see that the shaded region where the two regions overlap represents the solution to the system of linear inequalities.
