Class 9 Mathematics
Chapter 4: Linear Equations in Two Variables
Exercise 4.1 – Stepwise Solutions
Important Formula Used
The standard form of a linear equation in two variables is:
ax + by + c = 0
where a, b and c are real numbers, and a and b are not both zero.
Q1. The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement.
Given:
Cost of a notebook = ₹x
Cost of a pen = ₹y
According to the question:
The cost of a notebook is twice the cost of a pen.
So,
x = 2y
This is the required linear equation.
If written in standard form:
x − 2y = 0
Q2. 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
Bring all terms to one side:
2x + 3y − 9.35 = 0
So, a = 2, b = 3, c = −9.35
(ii) x − y/5 − 10 = 0
This is already in the form ax + by + c = 0
So, a = 1, b = −1/5, c = −10
(iii) −2x + 3y = 6
Bring all terms to one side:
−2x + 3y − 6 = 0
So, a = −2, b = 3, c = −6
(iv) x = 3y
Bring all terms to one side:
x − 3y = 0
So, a = 1, b = −3, c = 0
(v) 2x = −5y
Bring all terms to one side:
2x + 5y = 0
So, a = 2, b = 5, c = 0
(vi) 3x + 2 = 0
Write y term as 0y:
3x + 0y + 2 = 0
So, a = 3, b = 0, c = 2
(vii) y − 2 = 0
Write x term as 0x:
0x + y − 2 = 0
So, a = 0, b = 1, c = −2
(viii) 5 = 2x
Bring all terms to one side:
2x − 5 = 0
Write y term as 0y:
2x + 0y − 5 = 0
So, a = 2, b = 0, c = −5