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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:
x |
0 |
50 |
100 |
y |
100 |
50 |
0 |
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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