Solve the system of inequalities by graphing.
y ≤ -1/3 x + 7
y ≥ -x + 5
To graph the system of inequalities, we first graph each inequality separately and then shade the region that satisfies both inequalities.
1. Graphing y ≤ -1/3 x + 7:
- To graph this inequality, we plot the y-intercept of 7 and then use the slope (-1/3) to find more points on the line. We draw a solid line because the inequality includes "less than or equal to".
- The line passes through the points (0,7), (-3,8), and (-6,9).
2. Graphing y ≥ -x + 5:
- To graph this inequality, we plot the y-intercept of 5 and then use the slope (-1) to find more points on the line. We draw another solid line because the inequality includes "greater than or equal to".
- The line passes through the points (0,5), (1,4), and (6,-1).
After we have graphed both inequalities, we shade the region where the shaded regions overlap, indicating the solution to the system of inequalities.
The shaded region includes the area above the line y = -x + 5 and below the line y = -1/3 x + 7. The shaded region is below the intersection of the two lines.
Here is the graph of the system of inequalities:
https://www.desmos.com/calculator/x9top0ugb1