Solve the system of inequalities by graphing.
y < 3x +3
3x-y ≤ 4
To graph the system of inequalities, let's start by graphing each inequality separately.
First, let's graph the inequality y < 3x + 3.
1. Start by graphing the line y = 3x + 3. To do this, plot the points (0, 3) and (1, 6) and draw a line passing through these points.
2. Since the inequality is y < 3x + 3, the line is not included in the solution. Therefore, we will use a dashed line to indicate this.
3. To determine which side of the line to shade, choose a point not on the line and substitute its x and y coordinates into the inequality. For example, let's choose the point (0, 0).
Substitute x = 0 and y = 0 into the inequality: 0 < 3(0) + 3
Simplify: 0 < 3
Since 0 is less than 3, the point (0, 0) is in the shaded region below the dashed line.
Next, let's graph the inequality 3x - y ≤ 4.
1. Start by graphing the line 3x - y = 4. To do this, plot the points (0, -4), (-2, -10), and (2, 2) and draw a line passing through these points.
2. Since the inequality is 3x - y ≤ 4, the line and the region below it are included in the solution. Therefore, we will use a solid line to indicate this.
3. To determine which side of the line to shade, choose a point not on the line and substitute its x and y coordinates into the inequality. For example, let's choose the point (0, 0).
Substitute x = 0 and y = 0 into the inequality: 3(0) - 0 ≤ 4
Simplify: 0 ≤ 4
Since 0 is less than or equal to 4, the point (0, 0) is in the shaded region below the solid line.
Now, let's put both graphs together and shade the overlapping region.
The shaded region below the dashed line from the first inequality and below the solid line from the second inequality represents the solution to the system of inequalities.
The final solution is the overlapping region below the dashed line y < 3x + 3 and the solid line 3x - y ≤ 4.
Note: The exact shape and position of the lines and the shaded region may vary depending on the accuracy of the graphing.