Class 9 Maths Ganita Manjari Chapter 13 Exercise 13.1 Solutions Two Variables, One Line

Class 9 Maths Ganita Manjari Chapter 13 Exercise 13.1 Solutions – Two Variables, One Line help students understand the basic concepts of linear equations in two variables. This exercise focuses on writing equations in standard form, identifying coefficients, representing real-life situations using two variables, and understanding how different values satisfy a linear equation.

The step-by-step solutions make the concepts easier to understand and help students practise the fundamentals required for solving more advanced problems in the chapter.

Class 9 Maths Ganita Manjari Chapter 13 Exercise 13.1 Solutions Two Variables, One Line

NCERT Class 9 Maths Ganita Manjari Chapter 13 Exercise Set 13.1

1. Write a linear equation in two variables in which a = 3, b = 0 and c = −1/5.

Answer:

The standard form of a linear equation in two variables is:

ax + by + c = 0

Given:
a = 3, b = 0, c = −1/5

Substituting these values:

3x + 0y − 1/5 = 0

Therefore, the required linear equation is:

3x − 1/5 = 0

2. Complete the following table after expressing the given linear equations in standard form.

Class 9 Maths Ganita Manjari Chapter 13 Exercise Set 13.1 Question 2

Answer:

The standard form of a linear equation in two variables is:

ax + by + c = 0

Linear equation in two variables Standard Form Coefficient of x Coefficient of y Constant term
y − 15 = √2x −√2x + y − 15 = 0 −√2 1 −15
3y − 2x = 0 −2x + 3y + 0 = 0 −2 3 0
5x = 3y 5x − 3y + 0 = 0 5 −3 0
x = 8 x + 0y − 8 = 0 1 0 −8
3y = 1 0x + 3y − 1 = 0 0 3 −1

Thus, each equation has been rewritten in the form ax + by + c = 0, and the corresponding coefficients of x, y, and the constant term have been identified.

3. (i) The cost of a notebook is twice the cost of a pen. Consider the cost of a notebook to be ₹t and that of a pen to be ₹p. Charlie wrote t = 2p, whereas Meera wrote p = 2t. Which of these two representations is correct? (ii) In a one-day International Cricket match between India and Sri Lanka played in Nagpur, two Indian batsmen together scored 176 runs. Manisha expressed this situation as x + y = 176, where the number of runs scored by one batsman is x, and the number of runs scored by the other is y. Is this a correct representation?

Answer:

(i)

The cost of a notebook is twice the cost of a pen.

Let:

  • Cost of a notebook = ₹t
  • Cost of a pen = ₹p

Therefore,

t = 2p

So, Charlie’s representation is correct.

Meera’s equation p = 2t would mean that the cost of a pen is twice the cost of a notebook, which is not given.

(ii)

Let:

  • Runs scored by one batsman = x
  • Runs scored by the other batsman = y

Together, they scored 176 runs.

Therefore,

x + y = 176

Hence, Manisha’s representation is correct.

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