Chapter 1
Linear Equations and Graphing
Course: Gre
Subject: Gre Quantitative Reasoning
Chapter: Inequalities And Absolute Values
What Is a System of Inequalities?
A system of inequalities consists of two or more inequalities considered together. The solution to a system is the set of all points that satisfy every inequality in the system simultaneously. Graphically, this is represented by the overlapping region where the shaded areas of all individual inequalities intersect.
Unlike equations, where a system often has a single solution point, systems of inequalities typically have entire regions of solutions—sometimes bounded (closed shapes like triangles) and sometimes unbounded (infinite regions).
Steps to Solve and Graph a System of Inequalities
| Step | Action | | 1 | Graph each inequality separately on the same coordinate plane | | 2 | Use a solid line for ≤ or ≥ (inequalities that include equality) | | 3 | Use a dashed line for < or > (strict inequalities) | | 4 | Shade the appropriate side for each inequality (test a point if needed) | | 5 | Identify the overlapping region where all shadings intersect | | 6 | The overlapping region is the solution to the system |