Linear equation: Difference between revisions
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In [[mathematics]], or more specifically [[algebra]], a '''linear equation''' is an [[equation]] in which each term is either a [[constant]] or the [[multiplication|product]] of a constant with a variable. In other words, a linear equation equates [[polynomials]] of the first | In [[mathematics]], or more specifically [[algebra]], a '''linear equation''' is an [[equation]] in which each term is either a [[constant]] or the [[multiplication|product]] of a constant with a variable. In other words, a linear equation equates [[polynomials]] of the first degree. | ||
Linear equations are ubiquitous in [[applied mathematics|application]]s of mathematics. They appear in the simplest problems where one unknown quantity needs to be determined from other given information. They can always be [[solution (equation)|solved]], and are the simplest equations to solve, requiring only the elementary [[operation (mathematics)|operation]]s of elementary arithmetic ([[addition]], [[subtraction]], [[multiplication]], and [[division]]) and their properties. | Linear equations are ubiquitous in [[applied mathematics|application]]s of mathematics. They appear in the simplest problems where one unknown quantity needs to be determined from other given information. They can always be [[solution (equation)|solved]], and are the simplest equations to solve, requiring only the elementary [[operation (mathematics)|operation]]s of elementary arithmetic ([[addition]], [[subtraction]], [[multiplication]], and [[division]]) and their properties. | ||
Many other types of equations (called '''non-linear''' equations) cannot be solved exactly. Linear equations are important for finding approximate solutions when exact solutions cannot be obtained. | Many other types of equations (called '''non-linear''' equations) cannot be solved exactly. Linear equations are important for finding approximate solutions when exact solutions cannot be obtained. | ||
Revision as of 13:37, 17 December 2008
In mathematics, or more specifically algebra, a linear equation is an equation in which each term is either a constant or the product of a constant with a variable. In other words, a linear equation equates polynomials of the first degree.
Linear equations are ubiquitous in applications of mathematics. They appear in the simplest problems where one unknown quantity needs to be determined from other given information. They can always be solved, and are the simplest equations to solve, requiring only the elementary operations of elementary arithmetic (addition, subtraction, multiplication, and division) and their properties.
Many other types of equations (called non-linear equations) cannot be solved exactly. Linear equations are important for finding approximate solutions when exact solutions cannot be obtained.