Algebra
- Algebra is a branch of mathematics in which Arithmetic is generalised.
- We use lower case English alphabets called literals to represent quantities instead of particular numbers. Literals are also used for representing unknown quantities.
- Literals take different values according to the problem. So, they are called variables.
- Constant: A symbol having a fixed value is called a constant. Usually all numbers are constants. But sometimes, 'c', 'k' etc., are used as symbols to denote constant.
- Coefficient: In the product of a variable and a constant, each is called the coefficient of the other. Sometimes, letters such as a, b,\[l\], m etc., are used to denote the coefficients. If the coefficient is a number, then it is called the numerical coefficient.
- Algebraic expression: A combination of constants and variables connected by some or all of the four fundamental operations +, -, x and - is called an algebraic expression.
e.g., 3y – 14
- Here, 3 is the coefficient of\['y','y'\] is the variable and -14 is the constant.
- Terms of an algebraic expression: The different parts of the algebraic expression separated by the sign + or -, are called the terms of the expression.
e.g., \[6-5x+3{{x}^{2}}y\]is an algebraic expression consisting of three terms, namely 6, - 5\[x\] and
\[3{{x}^{2}}y\].
- Equation: A statement of equality of two algebraic expressions involving one or more variables is called an equation.
e.g., \[3x-5=4x+7,2p+3q-5=16\]etc.
- Solution of an equation: The value of the variable, which when substituted in the given equation, makes the two sides [L.H.S. (Left Hand Side) and R.H.S. (Right Hand Side)] of the equation equal is called the solution of the equation.
\[3x+2=14\Rightarrow 3x=14\text{ - }2\text{ }\Rightarrow 3x=12\text{ }\Rightarrow x=l2=4\]\[\therefore \]4 is the solution or root of the given equation.
- Trial and error method: This method is used to find the solution of an equation. In this method, we give different values to the variable and check if they satisfy the equation. We continue the process of giving values to the variable until we find a value that satisfies the equation.
