The system of inequalities that represents the above problem is:
x + y ≤ 15 ; 17x + 10y ≥ 200. Minimum income constraint: Bashir must earn at least $200, so: 17x + 10y ≥ 200.
Total hours constraint: Bashir can work no more than 15 hours in a week, so: x + y ≤ 15
To solve this graphically, plot the first inequality, x + y ≤ 15. Remember to convert the inequality to an equality first (e.g., x + y = 15) and then plot the line. Shade the area below the line as this represents valid combinations of hours where the total is less than or equal to 15.
Plot the second inequality, 17x + 10y ≥ 200. Again, convert it to an equality (e.g., 17x + 10y = 200) and plot the line.
Shade the area above the line as this represents valid combinations of hours where the income is greater than or equal to $200.
Note that the area where the shaded regions overlap is the region where both constraints are satisfied, representing possible solutions for Bashir's hours.
Full Question:
Although part of your question is missing, you might be referring to this full question:
Bashir is working two summer jobs, making $17 per hour lifeguarding and making $10 per hour washing cars. In a given week, he can work no more than 15 total hours and must earn at least $200. If x represents the number of hours lifeguarding and y represents the number of hours washing cars, write and solve a system of inequalities graphically and determine one possible solution.