Solve the system of inequalities by graphing.

Question

y < 3x + 5

3x - y <= 4

Answer 1

To graph the system of inequalities, we start by graphing each inequality separately.

First, let's graph the inequality y < 3x + 5. To do this, we plot the line y = 3x + 5 as a dashed line since the inequality is strict (less than), and shade the region below the line.

The y-intercept is (0,5) and the slope is 3, so we can plot two more points: (-1, 2) and (1, 8) and draw a line passing through these points.

Next, let's graph the inequality 3x - y <= 4. To do this, we plot the line 3x - y = 4 as a solid line since the inequality is not strict (less than or equal to), and shade the region below the line.

To graph this line, we can find two points: (0, -4) and (2, 2) and draw a line passing through these points.

Here is the graph of the system of inequalities:
[Note: The graph cannot be represented as a text. Please refer to the image attached in your question or your textbook/materials.]

The shaded region where the two regions overlap is the solution to the system of inequalities.