systems

# systems

of linear equations

Systems of linear equations are a set of two or more equations with two or more variables that are used to describe relationships between different quantities. Systems of linear equations are used in a variety of disciplines, from mathematics to economics to engineering.

A linear equation is an equation of the form ax + b = c, where a, b, and c are constants, and x is the variable. A system of linear equations is a set of two or more linear equations with two or more variables. For example, a system of two linear equations with two variables would be written as follows:

ax + by = c

dx + ey = f

In this system, a, b, c, d, e, and f are all constants, and x and y are the variables.

To solve a system of linear equations, you must find a set of values for the variables that make all the equations true. This is done by using a variety of methods, including substitution, elimination, and graphing.

Substitution involves solving one of the equations for one of the variables and then substituting the value of the variable into the other equation. This can be used to solve for both variables.

Elimination involves adding or subtracting the equations to eliminate one of the variables. This can also be used to solve for both variables.

Graphing involves plotting the equations on a graph and then finding the point of intersection. This can be used to solve for both variables.

Systems of linear equations are used in a variety of disciplines to describe relationships between different quantities. For example, in economics, systems of linear equations are used to model supply and demand. In engineering, systems of linear equations are used to model the behavior of electrical circuits.

In mathematics, systems of linear equations are used to solve problems involving linear equations. They can also be used to solve problems involving linear inequalities, which are equations with the inequality symbol (e.g., >, <, ≥, ≤). Systems of linear equations are an important tool for solving a variety of problems in mathematics, economics, and engineering. They can be used to model relationships between different quantities, and to solve problems involving linear equations and linear inequalities.