The solution to the system of inequalities is the shaded region between the two lines. A graph of the same is attached below
To solve the system of inequalities y < 5x - 5 and y > 5x + 9, you can follow these steps:
1. Graph each inequality separately:
Start by graphing each inequality on the coordinate plane.
a. Graph y < 5x - 5:
- Plot the y-intercept at (0, -5).
- Use the slope of 5 to find another point (e.g., go up 5 units and to the right 1 unit).
- Draw a dashed line since (y) is less than (not equal to) the expression.
b. Graph y > 5x + 9:
- Plot the y-intercept at (0, 9).
- Use the slope of 5 to find another point.
- Draw a dashed line since y is greater than (not equal to) the expression.
2. Identify the solution region:
The solution to the system is the region where the shaded regions of the two inequalities overlap. Since (y) is less than (5x - 5) and greater than (5x + 9), the solution lies between the two lines.
3. Determine the shaded region:
Shade the area where the solutions overlap. This region represents the solution to the system.
Below is the graph attached