In Problems 23-34, graph each system of linear inequalities....

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Key Concepts

Intersection of Regions

For a system of inequalities, the solution is found by identifying the common area where all the individual regions overlap. This intersection, often called the feasible region, represents the set of all solutions that simultaneously satisfy every inequality in the system.

Boundary Lines

The boundary line of a linear inequality is obtained by converting the inequality into an equation. Depending on whether the inequality is strict (using < or >) or non-strict (using ? or ?), the boundary line may be represented as dashed or solid, respectively, indicating whether points on the line are included in the solution set.

System of Linear Inequalities

This concept involves multiple inequalities that must be satisfied simultaneously by a set of variable values. In algebra, solving a system of linear inequalities requires determining the intersection of the solution sets of each inequality, which represents all points that meet every condition at the same time.

Graphical Representation of Inequalities

Graphing inequalities involves plotting the equality case as a boundary line on a coordinate plane, and then shading the region that satisfies the inequality condition. This visual representation helps in understanding and identifying the set of solutions.

In Problems 23-34, graph each system of linear inequalities. $\left\{\begin{array}{l}x-4 y \leq 4 \\ x-4 y \geq 0\end{array}\right.$

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