Linear Equations
NCERT Solutions • Class 9 Maths • Chapter 4Exercise 4.1
1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
Let the cost of a notebook be $x$ and that of a pen be $y$.
According to the given condition:
Cost of Notebook = 2 × Cost of Pen
$x = 2y$
Rearranging the terms:
Equation: $x – 2y = 0$
According to the given condition:
Cost of Notebook = 2 × Cost of Pen
$x = 2y$
Rearranging the terms:
Equation: $x – 2y = 0$
2. Express the following linear equations in the form $ax + by + c = 0$ and indicate the values of $a, b$ and $c$ in each case:
(i) $2x + 3y = 9.35$
Rewrite as: $2x + 3y – 9.35 = 0$
a = 2 b = 3 c = -9.35
Rewrite as: $2x + 3y – 9.35 = 0$
a = 2 b = 3 c = -9.35
(ii) $x – \frac{y}{5} – 10 = 0$
Equation is already in form: $1x + (-\frac{1}{5})y + (-10) = 0$
a = 1 b = -\frac{1}{5} c = -10
Equation is already in form: $1x + (-\frac{1}{5})y + (-10) = 0$
a = 1 b = -\frac{1}{5} c = -10
(iii) $-2x + 3y = 6$
Rewrite as: $-2x + 3y – 6 = 0$
a = -2 b = 3 c = -6
Rewrite as: $-2x + 3y – 6 = 0$
a = -2 b = 3 c = -6
(iv) $x = 3y$
Rewrite as: $x – 3y + 0 = 0$
a = 1 b = -3 c = 0
Rewrite as: $x – 3y + 0 = 0$
a = 1 b = -3 c = 0
(v) $2x = -5y$
Rewrite as: $2x + 5y + 0 = 0$
a = 2 b = 5 c = 0
Rewrite as: $2x + 5y + 0 = 0$
a = 2 b = 5 c = 0
(vi) $3x + 2 = 0$
Rewrite as: $3x + 0y + 2 = 0$
a = 3 b = 0 c = 2
Rewrite as: $3x + 0y + 2 = 0$
a = 3 b = 0 c = 2
(vii) $y – 2 = 0$
Rewrite as: $0x + 1y – 2 = 0$
a = 0 b = 1 c = -2
Rewrite as: $0x + 1y – 2 = 0$
a = 0 b = 1 c = -2
(viii) $5 = 2x$
Rewrite as: $2x + 0y – 5 = 0$
a = 2 b = 0 c = -5
Rewrite as: $2x + 0y – 5 = 0$
a = 2 b = 0 c = -5