Yamini and Fatima, two students of Class IX of a school, together contributed ₹ 100 towards the Prime Minister’s Relief Fund to help the earthquake victims. Write a linear equation which satisfies this data. (You may take their contributions as ₹ x and ₹ y.) Draw the graph of the same.

Solution:

We can assume Yamini and Fatima's contributions as ₹ x and ₹ y respectively, and form a linear equation.

• Let the amount that Yamini and Fatima have contributed individually be ₹ x and ₹ y respectively towards the Prime Minister’s Relief Fund.
• The total amount contributed by Yamini and Fatima together is = ₹ 100

Therefore, x + y = 100

On transposing, y = 100 - x

This is a linear equation in two variables of the form ax + by + c = 0

• Let us consider this y = 100 - x  ---  Equation (1)

By substituting different values of x in the equation (1), we get different values for y

• When x = 0, y = 100
• When x = 50, y = 50
• When x = 100, y = 0

Thus, we have the following table with all the obtained values of x and y:

The graph of the line represented by the given equation is as shown.

Here, variables x and y are representing the amount contributed by Yamini and Fatima respectively and these quantities cannot be negative. Hence, only those values of x and y which are lying in the 1^st quadrant are considered.

☛ Check: NCERT Solutions Class 9 Maths Chapter 4

Video Solution:

Yamini and Fatima, two students of Class IX of a school, together contributed ₹ 100 towards the Prime Minister’s Relief Fund to help the earthquake victims. Write a linear equation which satisfies this data. (You may take their contributions as ₹ x and ₹ y.) Draw the graph of the same

NCERT Solutions Class 9 Maths Chapter 4 Exercise 4.3 Question 7

Summary:

If Yamini and Fatima, two students of Class IX of a school, together contributed ₹ 100 towards the Prime Minister’s Relief Fund to help the earthquake victims, then a linear equation which satisfies this data is given by x + y = 100 where their contributions as ₹ x and ₹ y respectively.

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