# 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.

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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,

Updated on 10-Oct-2022 13:40:12