Complete Reference Guide for Class 9 Mathematics
Prepared by Muhammad Tayyab (SSE Math)
Govt. Christian High School Daska
Linear Equations · Inequalities · Feasible Region · Optimization · Problem Constraints
Class 9 Mathematics | Punjab Curriculum and Textbook Board Syllabus 2025
An equation of the form \( ax + b = 0 \), where \( a \) and \( b \) are constants, \( a \neq 0 \), and \( x \) is a variable, is called a linear equation in one variable.
General Form: \( ax + b = 0 \), where \( a \neq 0 \)
Note: The highest power of the variable in a linear equation is always 1.
A mathematical statement that expresses a relationship between two expressions that are not equal.
A linear inequality in one variable \( x \) is of the form:
\( ax + b < 0 \), where \( a, b \in \mathbb{R} \), \( a \neq 0 \)
Note: The \( < \) symbol can be replaced by \( > \), \( \leq \), or \( \geq \).
In real-world problem solving, each linear inequality associated with a particular problem is called a problem constraint.
The collection of these linear inequalities for a given problem is referred to as problem constraints.
The variables used in systems of inequalities must satisfy non-negative constraints (zero or positive values). These variables are crucial for decision-making and are called decision variables.
The area confined to the first quadrant that satisfies all given constraints is known as the feasible region.
Every point within the feasible region represents a valid feasible solution to the system of linear inequalities.
A point of a solution region where two boundary lines intersect is called a corner point or vertex of the solution region.
A function which is to be maximized or minimized is called an objective function.
The feasible solution which maximizes or minimizes the objective function is called the optimal solution.
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