TopMathematics is a vast Combination of equations, ratios, trigonometry, geometry etc. and one of the forms is equations. The equations used in mathematics makes the calculations quiet easier and simple for the users. It provides a proper sequence of solving any problem. An equation is defined as a mathematical statement that asserts the quality of two expressions. In modern notation this is written by placing the expressions on both the sides of an equal sign. Represented by ‘=’

X+2=5

This is an equation, where x is a variable and whose value of x is to be determined.

X=5-2

X=3

Equation plays a crucial role in modern mathematics and form the basis for mathematics modeling of numerous phenomenon and processes in science and engineering. Let’s discuss about types of equations:

Algebraic equations: an equation involving only algebraic expressions.

Linear equations: an algebraic equation of degree one.

Polynomial equations: an equation in which a polynomial is Set equal to another polynomial.

Functional equations: an equation in which the unknown are Functions rather than simple quantities.

Differential equations: an equation involving Derivatives.

Integral equations: an equation involving integrals.

Quadratic equations

PROPERTIES of Equation:

Any real number can be added and subtracted to both the sides.

Any real number can be multiplied to both the sides.

Any non-zero real number can be divided from both the sides.

Some Functions can be applied to both the sides.

Now the big question comes in our mind is that how to solve equations? Now here in this session we will learn how to solve equations of different types. Let’s take an example: We want to solve an equation in one variable and the equation provided as

4x +2 =10

Then,

The value of x can be determined as

4x=10-2

4x=8

X=8/4

X=2

Equation in one variable is defined as the equation which contains only one variable. Equation in two one variable is defined as the equation which contains two variables in it. It can be solved by using the substitution method. That one variable is replaced by the other variable.

For example:

x+3y=10.

On using substitution method,

Put x=1 and y=3 we get,

1+3*3

=10=RHS.

Hence the values of x and y are 1 and 3 respectively.