Maths Chapter 02: Linear Equations in One Variable

Class 08 Maths NCERT

In the earlier classes, you have come across several algebraic expressions and equations. Some examples of expressions we have so far worked with are: 5x, 2x – 3, 3x + y, 2xy + 5, xyz + x + y + z, x² + 1, y + y²

Some examples of equations are:

5x = 25, 2x - 3 = 9, 2y + 5/2 = 37/5

You would remember that equations use the equality (=) sign; it is missing in expressions.

Of these given expressions, many have more than one variable. For example, 2xy + 5 has two variables. We however, restrict to expressions with only one variable when we form equations. Moreover, the expressions we use to form equations are linear. This means that the highest power of the variable appearing in the expression is 1.

An algebraic equation is an equality involving variables. It says that the value of the expression on one side of the equality sign is equal to the value of the expression on the other side.

Linear equations in one variable: In such equations, the expressions which form the equation contain only one variable. Further, the equations are linear, i.e., the highest power of the variable appearing in the equation is 1.

A linear equation may have for its solution any rational number. Just as numbers, variables can, also, be transposed from one side of the equation to the other. Occasionally, the expressions forming equations have to be simplified before we can solve them by usual methods. Some equations may not even be linear to begin with, but they can be brought to a linear form by multiplying both sides of the equation by a suitable expression.

The utility of linear equations is in their diverse applications; different problems on numbers, ages, perimeters, combination of currency notes, and so on can be solved using linear equations.