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 solve the system of inequalities by graphing, we will graph the lines y = -3 and y = -2x - 5 and shade the region below both lines.
First, let's graph the line y = -3. Since the inequality symbol is "less than or equal to," the line will be solid.
-3 will be on the y-axis.
Now, let's graph the line y = -2x - 5. Since the inequality symbol is "less than or equal to," the line will also be solid.
To graph this line, we can find the x and y-intercepts:
For x-intercept, let y = 0
0 = -2x - 5
2x = -5
x = -5/2 or -2.5
For y-intercept, let x = 0
y = -2(0) - 5
y = -5
Now, we can plot the two lines on a graph:
The line y = -3 will be a horizontal line passing through the point (0, -3).
The line y = -2x - 5 will pass through the points (0, -5) and (-2.5, 0).
Next, we need to shade the region below both lines, as the solution to the system of inequalities will be in that shaded region.
Hence, the solution to the system of inequalities is the shaded region below both lines.