Page 149 - ICSE Math 7

13 Linear Equations in

One Variable

Key Concepts

• Equation • Rules for Solving an Equation
• Solution of a Linear Equation • Transposing a Term of an Equation
• Trial and Error Method • Applications of Linear Equations

In this chapter, we will discuss the methods of solving linear equations in one variable and applications
of linear equations.

Equation
An equation is a mathematical statement which shows the equality of two expressions. In an equation,
there is always an equality sign (=) which shows that the value of expression on the left hand side of
the sign is equal to the value of expression on the right hand side . In fact, an equation is a condition
on a variable. The condition is that the two expressions of which at least one contains a variable are
2
2
equal. For example, 2x + 3 = 7, 3x + 4y = 10, x = 1, 3x + y = 4 are equations.
Simple Equation
An equation having only one variable is known as simple equation. A simple equation having
variable with highest power one is known as a simple linear equation. For example, 3x + 4 = 13 and
2x + 4 = 5x are simple equations.

Linear Equation
An equation having variables with the highest power one is known as linear equation. For example,
3m + n = 5, 4x + y = x + 5, 2a + b = 3 are linear equations.

Linear equation in one variable

An equation which has only one variable with the highest power one is known as linear equation in
one variable or a simple linear equation. For example, 2a + 5 = 7, 3x + 7 = 12 and m + 7 = 3m are
simple linear equations.
Solution of a Linear Equation

The value of the variable which satisfies the given linear equation, i.e., makes the statement true is
called the solution or the root of the linear equation.

Example 1: Check whether the value given in the brackets is the solution to the given equation or not:

(a) 2y + 3 = 21; (y = –9) (b) n – 4 = –2; (n = 6)
3
Solution: (a) On putting y = –9, LHS = 2(–9) + 3 = –15 ≠ 21 = RHS
∴ y = –9 is not the solution of the given equation.
6
n
(b) On putting n = 6, LHS = – 4 = – 4 = –2 = RHS
3 3
∴ n = 6 is the solution of the given equation.

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