Systems of Equations and Inequalities

This course's main objective is to discuss the Systems of Equations and Inequalities. The course starts with the concept of Solving a system of equations by the graphical method and by the substitution method. The course gives the details of Solving a system of equations by the elimination method. The course includes a discussion of Solving a system of linear equations in three variables. The course derives the Classification of systems as consistent and inconsistent. The course concludes with the study of solving nonsquare systems, Interpretation of linear systems in three variables geometrically, and Use linear systems in applications. The course gives details about the Partial–Fraction Decomposition, Systems of Nonlinear Equations, Systems of Inequalities, Linear Programming, and Use of linear programming in applications.

6 topics

235 lectures

Educators

Course Curriculum

Introduction to Algebra

60 videos

Linear Functions

35 videos

Solve Linear Inequalities

35 videos

20 videos

Graph Linear Functions

40 videos

Write Linear Equations

45 videos

Systems of Equations and Inequalities Lectures

Systems of Equations and Inequalities

Graphing System of Inequalities - Example 1

In mathematics, a system of linear equations is a group of linear equations with the same number of unknowns. A system of linear equations is a group of linear equations with the same number of unknowns. A system of linear equations is a group of linear equations with the same number of unknowns.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Equationsby Graphing - Example 2

In mathematics, graphing is a method for visualizing functions and relations in order to analyze them. It is also used to study a function's properties and, in some cases, to approximate the function.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Equationsby Elimination - Example 1

In mathematics, elimination or Gaussian elimination is an algorithm for solving systems of linear equations. It can be used to solve a system of equations in which all the unknowns are scalars, or to solve a system of equations in which all the unknowns are vectors. It is a special case of Gaussian substitution.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Equationsby Elimination - Example 2

In mathematics, elimination or Gaussian elimination is an algorithm for solving systems of linear equations. It can be used to solve a system of equations in which all the unknowns are scalars, or to solve a system of equations in which all the unknowns are vectors. It is a special case of Gaussian substitution.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Equationsby Graphing - Example 4

In mathematics, graphing is a method for visualizing functions and relations in order to analyze them. It is also used to study a function's properties and, in some cases, to approximate the function.

Whitney Dillinger

Systems of Equations and Inequalities

Graphing System of Inequalities

In mathematics, a system of inequalities is a collection of inequalities contained in a set of linear equations. The solution set of such a system is the set of all real numbers that make all of the inequalities true simultaneously.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Equationsby Elimination

In mathematics, a system of equations is a set of simultaneous equations. In the most common case, the variables are unknowns and the equations describe properties of the variables. Systems of equations arise naturally in all branches of applied mathematics, and also in other fields, such as physics and economics. They are also central to the study of algorithms, where the goal is to find a solution to a system of equations, and to the study of mathematical logic, where the goal is to prove that such a solution exists. A system of equations is a set of equations, each of which is an instance of a variable. The variables are said to be "unknowns", and the equations describe properties of the variables. Systems of equations arise naturally in all branches of applied mathematics, and also in other fields, such as physics and economics. They are also central to the study of algorithms, where the goal is to find a solution to a system of equations, and to the study of mathematical logic, where the goal is to prove that such a solution exists.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Equationsby Substitution

In mathematics, substitution is a method of solving a system of linear equations. It consists in finding a solution of the system of equations by replacing the unknowns by new unknowns.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Equationsby Graphong - Example 1

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A "graph" in this context is made up of "vertices", "edges", and "faces". The vertices are also called "nodes" or "points". An edge is a line segment connecting two vertices. A face is a polygon connecting three or more vertices. Graphs are one of the prime objects of study in discrete mathematics.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Equationsby Substitution - Example 1

In mathematics, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning. The concept of algorithm has existed for centuries; however, a partial formalization of what would become the modern algorithm began with attempts to solve the Entscheidungsproblem (the "decision problem") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define "effective calculability" or "effective method"; those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, and Alan Turing's Turing machines of 1936–7 and 1939.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Equationsby Substitution - Example 2

In mathematics, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning. The concept of algorithm has existed for centuries; however, a partial formalization of what would become the modern algorithm began with attempts to solve the Entscheidungsproblem (the "decision problem") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define "effective calculability" or "effective method"; those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, and Alan Turing's Turing machines of 1936–7 and 1939.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Equationsby Elimination - Example 3

In mathematics, elimination or Gaussian elimination is an algorithm for solving systems of linear equations. It can be used to solve a system of equations in which all the unknowns are scalars, or to solve a system of equations in which all the unknowns are vectors. It is a special case of Gaussian substitution.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Equationsby Graphing- Ex3

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices, nodes, or points which are connected by edges, arcs, or lines. A graph may be undirected, meaning that there is no distinction between the two vertices associated with each edge, or its edges may be directed from one vertex to another. Graphs are one of the prime objects of study in discrete mathematics. The underlying graph theory has many applications in science and engineering, including network theory, circuit theory and the 4-color theorem.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Equationsby Substitution - Example 3

In mathematics, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning. The concept of algorithm has existed for centuries; however, a partial formalization of what would become the modern algorithm began with attempts to solve the Entscheidungsproblem (the "decision problem") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define "effective calculability" or "effective method"; those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, and Alan Turing's Turing machines of 1936–7 and 1939.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Equationsby Elimination - Example 4

In mathematics, elimination or Gaussian elimination is an algorithm for solving systems of linear equations. It can be used to solve a system of equations in which all the unknowns are scalars, or to solve a system of equations in which all the unknowns are vectors. It is a special case of Gaussian substitution.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Equationsby Substitution - Example 4

In mathematics, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning. The concept of algorithm has existed for centuries; however, a partial formalization of what would become the modern algorithm began with attempts to solve the Entscheidungsproblem (the "decision problem") posed by David Hilbert in 1928. Subsequent formalizations were framed as attempts to define "effective calculability" or "effective method"; those formalizations included the Gödel–Herbrand–Kleene recursive functions of 1930, 1934 and 1935, Alonzo Church's lambda calculus of 1936, and Alan Turing's Turing machines of 1936–7 and 1939.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Linear Equationsby Graphing

In mathematics, a system of linear equations is a set of linear equations involving the same number of unknowns. If the system is in matrix form, it can be represented by a matrix equation, which can be solved by matrix methods. A system of linear equations is consistent if there is a solution to the equations.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Equationsin3 Variables

In mathematics, a system of equations is a collection of equations involving one or more unknowns. A system of equations is usually written as a matrix of equations. In a system of linear equations, the matrix is a matrix of coefficients, and the unknowns are the values of the variables. In a system of non-linear equations, the matrix is not a matrix of coefficients, and the unknowns are the values of the variables and the non-linear functions and expressions involving them.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Equationsin3 Variables - Example 1

In mathematics, a system of equations is a set of equations containing several variables. In mathematics, systems of linear equations are fundamental objects in linear algebra. A system of linear equations is a collection of linear equations involving one or more unknowns, or parameters, that must be solved simultaneously in order to determine the unknowns. The solution set of a system of linear equations is the set of all values that the unknowns can take, if the equations are satisfied. The solution set is sometimes called the free set of the system. A solution to a system of linear equations is a specific set of values for the unknowns that makes all the equations in the system true. If the system is consistent, then there always exists at least one solution to the system. If the system is inconsistent, then there is no solution to the system.

Whitney Dillinger

Systems of Equations and Inequalities

Graphing System of Inequalities - Example 2

In mathematics, a system of linear equations is a group of linear equations with the same number of unknowns. A system of linear equations is a group of linear equations with the same number of unknowns. A system of linear equations is a group of linear equations with the same number of unknowns.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Equationsin3 Variables - Example 2

In mathematics, a system of equations is a set of equations containing several variables. In mathematics, systems of linear equations are fundamental objects in linear algebra. A system of linear equations is a collection of linear equations involving one or more unknowns, or parameters, that must be solved simultaneously in order to determine the unknowns. The solution set of a system of linear equations is the set of all values that the unknowns can take, if the equations are satisfied. The solution set is sometimes called the free set of the system. A solution to a system of linear equations is a specific set of values for the unknowns that makes all the equations in the system true. If the system is consistent, then there always exists at least one solution to the system. If the system is inconsistent, then there is no solution to the system.

Whitney Dillinger

Systems of Equations and Inequalities

Graphing System of Inequalities - Example 3

In mathematics, a system of linear equations is a group of linear equations with the same number of unknowns. A system of linear equations is a group of linear equations with the same number of unknowns. A system of linear equations is a group of linear equations with the same number of unknowns.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Equationsin3 Variables - Example 3

In mathematics, a system of equations is a set of equations containing several variables. In mathematics, systems of linear equations are fundamental objects in linear algebra. A system of linear equations is a collection of linear equations involving one or more unknowns, or parameters, that must be solved simultaneously in order to determine the unknowns. The solution set of a system of linear equations is the set of all values that the unknowns can take, if the equations are satisfied. The solution set is sometimes called the free set of the system. A solution to a system of linear equations is a specific set of values for the unknowns that makes all the equations in the system true. If the system is consistent, then there always exists at least one solution to the system. If the system is inconsistent, then there is no solution to the system.

Whitney Dillinger

Systems of Equations and Inequalities

Graping System of Inequalities - Example 4

A system of equations is a collection of equations that are written in the same format, with the same variables. They are written in the form of "A = B", where "A" is the first equation, "B" is the second equation, etc. In a system of equations, there is a variable in each equation, and the variables are the same in each equation. In a system of inequalities, there is a variable in each inequality, and the variables are the same in each inequality.

Whitney Dillinger

Systems of Equations and Inequalities

Solving System of Equationsin3 Variables - Example 4

In mathematics, a system of equations is a set of equations containing several variables. In mathematics, systems of linear equations are fundamental objects in linear algebra. A system of linear equations is a collection of linear equations involving one or more unknowns, or parameters, that must be solved simultaneously in order to determine the unknowns. The solution set of a system of linear equations is the set of all values that the unknowns can take, if the equations are satisfied. The solution set is sometimes called the free set of the system. A solution to a system of linear equations is a specific set of values for the unknowns that makes all the equations in the system true. If the system is consistent, then there always exists at least one solution to the system. If the system is inconsistent, then there is no solution to the system.

Whitney Dillinger