Here are the essential concepts you must grasp in order to answer the question correctly.
Inequalities
Inequalities are mathematical expressions that show the relationship between two values when they are not equal. They use symbols such as '<', '>', '≤', and '≥' to indicate whether one side is less than, greater than, or equal to the other. In this context, inequalities help define the constraints on the variables x and y, allowing us to express conditions like 'at most' or 'does not exceed'.
Recommended video:
Systems of Inequalities
A system of inequalities consists of two or more inequalities that share the same variables. The solution to a system is the set of all points (x, y) that satisfy all inequalities simultaneously. Graphically, this is represented by the overlapping regions of the graphs of each inequality, which helps visualize the feasible solutions that meet all conditions.
Recommended video:
Graphing Inequalities
Graphing inequalities involves plotting the boundary lines of the inequalities on a coordinate plane and determining which side of the line represents the solution set. For linear inequalities, the boundary line is either solid (for '≤' or '≥') or dashed (for '<' or '>'). The shaded region indicates all possible solutions, allowing for a visual interpretation of the constraints imposed by the inequalities.
Recommended video: