Algebra: Systems of Equations and Inequalities

Study Notes

System of Linear Equations

Comprises two or more linear equalities involving the same variable.

System of Inequalities

Consists of two or more inequalities that share the same variable.

Break Even Point

The critical point where income equals expenses, indicating no profit or loss.

Consistent Systems

Defines a system with exactly one solution, indicating that the lines intersect at a single point.

Inconsistent Systems

Characterizes a system that has no solution, often resulting in parallel lines that never intersect.

Independent Systems

Describes a system with only one unique solution, where the lines cross at one point.

Dependent Systems

Refers to a system that has an infinite number of solutions, where the equations effectively describe the same line.

Substitution Method

A technique where one variable is expressed from one equation and substituted into another equation in the system.

Elimination Method

A strategy used to remove one variable by using subtraction between two equations, especially when they share the same coefficient.

Linear Programming

A mathematical method for determining the maximum or minimum value of a function subject to a set of inequalities, where each inequality represents a limitation or constraint.

Feasible Region

The area in a graph representing all possible solutions, defined by the vertices of the solution set for the inequalities.

Description

Test your knowledge on systems of linear equations and inequalities. This quiz covers key concepts such as break even points, consistent and inconsistent systems, and various methods of solving them. Challenge yourself to differentiate between dependent and independent systems as well.