Refers to a system of equations where each of them is an equation of the first degree. It is also known simply as linear system, in which its first degree polynomial form stands out, which also means that its unknowns are not raised to powers.
These equations have a large number of applications in economics as regards the study of the supply and demand, for this reason we explain what they are and their characteristics so that you have a solid idea about the linear equations.
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We must take into account that an equation is any expression in which the equality symbol is found and when This expression has only one term, it is known as a monomial, and from there they are known as binomials or polynomials. The linear equations with a variable they could be called as a polynomial equation of the first degree and they acquire this name since in analytic geometry they form a line.
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In this article you will find:
Analytic geometry
It is a part of the geometry that is in charge of the study of the singularities of figures in a determined plane or in space. Regardless of the type of geometry, be it descriptive or in space, it is fundamental in mathematics and in arithmetic, since these are also directly related to engineering, such as the equations linear.
Linear algebra
We can start by defining what is known as algebra, a mathematical branch that is oriented towards mathematical operations with signs, numbers and letters, and linear refers to what has to do with the line, so we can define linear algebra as the operations with signs and numbers on the line. He specializes in work on vectors and matrices, its beginnings and history dates back to the end of the 18th century.
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Vectorial space
To fully understand the linear equations it is necessary to be familiar with vector spaces, which are structures that appear when a set is not empty. In this vector space we find the vectors. Another important part of these equations are the matrices, which are a two-dimensional number set, which allow representing coefficients of these systems of equations.
Importance and usefulness of linear algebra
In the engineering world, many natural phenomena can lead to the field of linear equations and the approximations of a linear model. It is not only important in engineering, as it is also used in circuit construction, in telecommunications and in the space industry, for this reason it is important to know their concepts and features.
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What are symbols in linear equations and what are they used for?
As we mentioned, the use of numbers, symbols and letters is fundamental in the equations, they represent the different mathematical operations and the numbers on the other hand are constant. It is worth noting that the letters can be a representation of variables or constants, the first letters of the alphabet are used to represent constants and the last to represent variables.
Grouping and algebraic language
So that the operations carried out can be read and understood according to the correct formulation of the algebraic language, it is necessary that said grouping and sequence use grouping symbols, the most important of which are parentheses and square brackets, although braces and dashes are also frequently used horizontal.
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These horizontal lines or stripes are also known in the world of linear equations as links, often used to divide or represent roots.
For most the symbols of addition, subtraction or multiplication are well known, however, it is important to know that these signs are fundamental for the representation of linear equations. Many times the symbol used to multiply is left out or omitted and other times it is simply replaced by a period.
Priority of operations in a linear equation
To carry out these operations correctly, it is necessary to approach them in the correct way and to clear up unknowns, starting with the multiplications, the next operations to be carried out in the linear equations will be the divisions, leaving the sums and you subtract.
The order in which these mathematical operations will be performed is subject to the grouping symbols, starting with those operations within the same group.
Compatible systems
These systems of equations stand out because they are systems in which there is a solution and various systems derive from these, such as:
- A certain compatible system, they stand out for having an equal number of unknowns and equations, in addition to having a certain number of solutions.
- Indeterminate compatible system, it differs from the first by having infinite solutions, in addition to having a greater number of unknowns than the number of equations.
Incompatible systems
Systems without a possible solution are called incompatible and generally in this type of system the equations are greater than the unknowns. There are also equivalent systems, in which a solution can be applied to several systems.
Methods for system solution
These are some systems that exist apart from the linear system of equations that we have mentioned and have ways and methods of solving, among which the following stand out:
Substitution method
A widely used method, in which an equation is cleared as a function of the others for it to replace any other of the unknowns of the system and in this way solve it.
It is one of the first methods of solving equations taught in school and high school courses. of mathematics, however, very important in areas such as industrial engineering and other branches of engineering.
Method for solving linear equations
As we mentioned the linear equations, those that are formed by two equations and two unknowns, are solved by solving the same unknown in the two equations and later equalize them, in order to end up with a single equation to solve, from the which will be obtained the value of the unknown and will be replaced by any unknown within the system to determine the value of the other.
