Yamini and Fatima, two students of Class IX of a school, together contributed Rs. 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 $ Rs. x $ and Rs. y.) Draw the graph of the same.
Given:
Yamini and Fatima, two students of Class IX of a school, together contributed Rs. 100 towards the Prime Minister's Relief Fund to help the earthquake victims.
To do:
We have to write the linear equation which satisfies the given data.
Solution:
According to the question,
Let Yamini's donation be $Rs.\ x$ and Fathima's donation be $Rs.\ y$.
Therefore,
The linear equation which satisfies the given data is,
$x+y=100$
We know that,
To draw a graph of a linear equation in two variables, we need at least two solutions to the given equation.
To find the solutions to the given equation $x+y=100$.
Let us substitute $x=0, 50, 100$ and $y=100, 50, 0$ in equation $x+y=100$
For $x=0$ and $y=100$
$0+100=100$
$100=100$
For $x=50$ and $y=50$
$50+50=100$
$100=100$
For $x=100$ and $y=0$
$100+0=100$
$100=100$
Therefore,
$(0, 100), (50, 50)$ and $(100, 0)$ are three solutions of the equation $x+y=100$.
Hence,
The graph of the linear equation $x+y=100$ in two variables is,
![](/assets/questions/media/153848-64336-1658991215.png)
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