Final answer:
To graph the given system of inequalities, we need to plot and connect points for each inequality and shade the overlapping regions. The first inequality represents Linda's minimum weekly earnings, while the second inequality represents her maximum hours worked. The graph will show all the possible combinations of lifeguard and babysitting hours that satisfy Linda's requirements.
Step-by-step explanation:
To graph the given system of inequalities, we can divide it into two parts:
1. The first inequality is 15L + 10B > 120. This represents the condition that Linda needs to earn at least $120 per week. To graph this inequality, we can start by assuming that she only works as a lifeguard, which means the number of hours babysitting (B) is 0.
Then, we can plot points on the graph where L = 0, L = 1, L = 2, and so on, and connect these points with a dashed line to show all the possible lifeguard work hours. However, since the inequality is > (greater than), the shaded region should be above the line.
2. The second inequality is L + B < 30. This represents the condition that Linda does not want to work more than 30 hours per week. To graph this inequality, we can start by assuming that she only works as a babysitter, which means the number of hours lifeguarding (L) is 0.
Then, we can plot points on the graph where B = 0, B = 1, B = 2, and so on, and connect these points with a dashed line to show all the possible babysitting hours. Since the inequality is < (less than), the shaded region should be below the line.
The graph of the system of inequalities will be the overlapping shaded regions of the two inequalities. These shaded regions represent all the combinations of lifeguard and babysitting hours that satisfy Linda's requirements.