Final answer:
To graph the system of inequalities, graph the equations 3x - 5y = 15 and Y = -2/3x + 1 as boundary lines. Then, shade below the first line and above the second line, with the overlapping region being the solution.
Step-by-step explanation:
To find a graph that represents the solution to the given system of inequalities, firstly, we should graph each inequality on the same coordinate plane. For the inequality 3x - 5y < 15, we want to find the boundary line. To do that, we pretend the inequality is an equation: 3x - 5y = 15. We can then graph this line and because the inequality is less than (<), we'll shade below the line.
For the second inequality, Y > -2/3x + 1, again, we first graph the line as if it were an equation Y = -2/3x + 1. Since this inequality is greater than (Y >), we shade above the line. The solution to the system of inequalities will be the region where the shadings overlap.
While performing these steps, remember the properties of linear equations described in Figure 12.4: if b > 0, the line slopes upward; if b = 0, the line is horizontal; if b < 0, the line slopes downward. These properties can help us graph the lines correctly.