MINI LESSON
Graphing Systems of Linear Inequalities
A system of linear inequalities represents a region where all inequalities are true at the same time.
Each inequality creates a shaded half-plane on the coordinate plane.
The solution to the system is the overlapping shaded region.
Words like at least and at most help determine whether the inequality symbols are \(\ge\) or \(\le\).
Question 1
A tour bus can seat, at most, 48 passengers. An adult ticket costs $18 and a child ticket costs $12. The bus company must collect at least $650 to make a profit. If \(a\) represents the number of adult tickets sold and \(c\) represents the number of child tickets sold, which system of inequalities models this situation if they make a profit?