Page 148 - ICSE Math 6

an equation which consists of variables (literals) with highest power one. For example, 3x + 2y = 6,
2x + 8 = 2 and 4x + y = x + 3 are linear equations.
A linear equation with only one variable is called linear equation in one variable. For example,
2n + 3 = 7, x + 5 = 4x, etc.

Properties of equations

(a) If the same quantity is added to both the sides of an equation, then the sums are equal, i.e.,
if x = y, then x + z = y + z

(b) If the same quantity is subtracted from both the sides of an equation, then the differences are
equal, i.e.,
if x = y, then x – z = y – z
(c) If the same quantity is multiplied on both the sides of an equation, then the products are equal, i.e.,

if x = y, then xz = yz
(d) If both the sides of an equation are divided by the same non-zero quantity, then the quotients are
equal, i.e.,

x y
if x = y and z ≠ 0, then =
z z
Transposition of terms of an equation

A term on any side of the equation can be shifted to the other side of
the equation by changing its sign. This is known as transposition. Maths Info
For example, Transposing a term does not
(a) x + 5 = 7 ⇒ x = 7 – 5 (b) y – 8 = 3 ⇒ y = 3 + 8 affect the equation.

(c) 7m = 15 ⇒ m = 15 (d) n = 4 ⇒ n = 4 × 6
7 6

Solution of an equation
A value of the variable (used in the equation) which satisfies the given equation is known as the
solution of the equation. For example,

(a) The equation 3x – 5 = –2 has x = 1 as the solution because 3 × 1 – 5 = –2.
5x 5×6
(b) The equation = 10 has x = 6 as the solution because = 10.
3 3

Solving linear equations in one variable
To solve a linear equation in one variable, collect all the terms containing the variable (literal) on
one side of the equation and the constant terms on the other side. Then, divide both the sides of the
equation by the resulting coefficient of the variable.
Example 3: Solve the equations.
10x
(a) x + 6 = 10 (b) y + 3 = 1 – y (c) + 3 = 13
3
Solution: (a) x + 6 = 10
⇒ x = 10 – 6 (Transposing 6 to the other side)
⇒ x = 4

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