Linear equation with a single variable could be presented in its canonical (traditional) form as: Ax + B = C, where x represents the variable, while A, B and C stand for numeric constant, also called the coefficients of the equations. The definitive condition for the equation in order to be called linear is the highest degree of its variable x, which must be of the first degree. Correspondingly, quadratic equation would have the highest degree of two for its variable, and so on. Equation could have more than one variable, but the definition of linearity will stay the same, applied to all and every variables, contained by equation.
The term “linear” actually came from the fact, that the single equation with two variables (like: y=Ax+B) could be graphically interpreted as a straight line by using the orthogonal system of two coordinates.
Linear equations belong to the class of algebraic equations; correspondingly, the solution for the linear equations belongs to the set of algebraic numbers. In simple words, algebraic numbers could be represented by a single point on the number line (or as a point on the plane in case of complex numbers). It’s relevant to mentioned, that the solutions to the linear equations belong exclusively to the set of rational numbers. In a context of linear equation, there is no need to go further into the extended domains of irrationals, transcendental or complex numbers; these topics will be covered in separate article.
Solution to the linear equation
Linear equation with single variable: Ax+B=C has a simple solution: x = (C-B) / A
It could be solved by using various tool of trades: “paper-pencil-calculator” (it’s so XX century), or the dedicated online math problem solvers, as for example, the linear equation solver, available on a totally free basis. The online version of linear equation solver has rather intuitive user interface, providing exceptional accuracy on any platform: either desktop PC, or notebook/netbook, or even mobile Internet-enabled devices, such as Apple iPod Touch ™ or Microsoft Zune™ HD (see the sample screen shot, attached to the article). All you need is just to enter the numeric values corresponding to the coefficients A, B and C into appropriate text boxes and click the “=” screen button to get the result.
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