Algebra is perhaps one of the largest sections in Mathematics. It consists of geometry, analysis and number theory. If you consider it from an overall perspective, it can be referred to as the study of the various symbols in mathematics and the various rules that are used to manipulate these symbols. Algebra is often considered to be the thread among the various sections in mathematics.
At the basic level, it mostly consists of equation solving at an elementary stage. If an individual want to reach higher levels, there’s a lot more to algebra than simple equation solving. Higher level algebra consists of group theory, ring, field and so on. Though the higher level algebra doesn’t find much of applications in our day to day life, elementary algebra has numerous applications. It is even an essential part in the syllabus of an individual in the event that an individual is pursuing a career in mathematics, science, economics, medicine, engineering and so on. The application are seemingly countless at this point of time.
Are you or your students facing problems as far as your / their assignments are concerned? Well, if that’s the case, it is imperative that they understand the importance of these assignments as far as building of their academics is concerned. This will definitely ensure that you or your students solve your / their assignments with a lot of concentration and interest. To understand the importance of assignments, go through the article, “Are assignments really helpful for good academics?”
What are symbols?
Before we move on to the x, y, z discussion, it is extremely important to understand what they are. In mathematics, these alphabets are some commonly used symbols. Well, what are symbols? A symbol can be defined as a sign, work or a mark that signifies or indicates an idea, relationship or objects. Symbol ought to make things a lot easier for mathematicians.
All sorts of data processing, communication, encryption idea, etc. are achieved through the use of various symbols. Without the major mathematical symbols, it would not have been possible for individuals to carry out the various tasks in technical fields.
If you move on to the application of symbols in our day to day lives, red octagon would be a very common symbol on roads which is used to as a symbol for “STOP”. The various uses of these symbols find a wide range of applications in the lives of most individuals even if they are not aware of these algebraic symbols.
What are x – y – z?
Well, in the language of algebra, x, y and z are used as variables in order to represent quantities that are unknown. These are definitely not the primary symbols used in algebra. However, they do play an extremely important role as far as the various applications of algebra are concerned. There are various reasons as to why individuals mostly use x, y and z in algebra. Two of the major reasons are discussed in details below:
- Variables are mostly used for representing elements or quantities of elements that are not known to us. Well, these assumptions in turn enable us to find the actually value of the elements by carrying out the various operations on symbols themselves.
- The symbol ‘x’ in turn is used to represent unknown elements in our day to day lives as well. As a result, it has found its applications in mathematics in this manner. Sometimes, there may be more than one unknown element. Well, under such circumstances, subsequent variables of x, namely ‘y’ and ‘z’ are used along with ‘x’.
- Another major reason as to why x, y and z are predominantly used in the field of algebra is that they are the last three letters of the English alphabet. Another group of alphabets that are extensively used in the field of algebra are a, b and c. These alphabets under most circumstances play the same roles as of x, y and z.
- A major psychological reason behind the use of the English alphabets a, b and c in algebra is that they are the first three letters of the English alphabet. Though x, y and z are used more often than not, even a, b and c are used under certain circumstances.
Finding the value of these variables
Well, an equation can have a number of variables depending on the number of parameters involved. Depending on this, the equations of algebra are classified into linear, quadratic, simultaneous, etc. This section of the article will be predominantly focusing on solving equations with one variable.
- Linear equations:
These are simplest of all types of equations where only one variable (predominantly x) is involved. Since only one variable is involved, a single equation would suffice as far as finding the value of x goes. We must remove all numbers from left hand side of the equation by subsequent additions, subtractions, multiplications and divisions on both sides of the equation.
- Quadratic equations:
These are equations of single variable of order 2. This order represents the number of possible values of x, often referred to as the roots of the equation. Such an equation can be solved in two ways to be precise. The first is the middle term approach with is often used by most individuals. The second approach is by the use of Sridhar Acharya’s formula which gives both real and imaginary roots of a particular equation.