Solve the system of inequalities by graphing.
x≤3
y<4x–9
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 each inequality on the same coordinate plane and shade the overlapping region.
First, let's graph the inequality x ≤ 3.
The inequality x ≤ 3 represents a vertical line passing through x = 3. Since the inequality is ≤, we will draw a solid line.
Next, let's graph the inequality y < 4x - 9.
To graph this inequality, we will first graph the equation y = 4x - 9 as a dotted line. This line has a y-intercept of -9 and a slope of 4. Then, we will shade the region below the line since the inequality is <.
Here is the graph:
[Graph]
<img src="https://i.imgur.com/0nzLp5f.png" alt="graph" width="400"/>
The solution to the system of inequalities is the shaded region where the two lines overlap. The shaded region is below the dotted line y = 4x - 9 and to the left of the solid line x = 3.