Solve the system of inequalities by graphing.
y≤
–
3
y≤
–
2x–5
Select a line to change it between solid and dotted. Select a region to shade it.
To graph the system of inequalities, we will first graph the first inequality, y ≤ -3, and then graph the second inequality, y ≤ -2x - 5.
For the first inequality, y ≤ -3, we draw a horizontal dashed line at y = -3. Since y is less than or equal to -3, we shade the region below the line.
For the second inequality, y ≤ -2x - 5, we need to find the boundary line first. To do this, we set the inequality as an equation:
y = -2x - 5
This is a linear equation with a slope of -2 and a y-intercept of -5. We draw the line with a solid line because the inequality includes equality.
Next, we shade the region below the line since y is less than or equal to -2x - 5.
The shaded region where the two inequalities overlap is the solution to the system of inequalities.
Here is the graph:
[------------------(only half the dashed line)
[
[
[
__________________________________
-3 -2 -1 0 1 2 3
I apologize but I can not display the graph on a text-based forum, please refer to a graphing tool or software to see the visual representation of the solution to the system of inequalities.