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4. Linear Equations in Two Variables
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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.
Option A
Option B
Option C
Option D
Solution
Let the contribution of Yamini $=₹ x$ and the contribution of Fatima $=₹ y$
$\therefore$ We have $x+y=100$ $\Rightarrow$
$y=100-x$
Now, when $x=0, \quad y=100-0=100$
When $x=50$, $y=100-50=50 $ When $x=100$, $ y=100-100=0$
We get the following table :
| $x$ | $0$ | $50$ | $100$ |
| $y$ | $100$ | $50$ | $0$ |
For drawing the graph, plot the ordered pairs $(0,\,100)$, $(50,\,50)$ and $(100,\,0)$ on a graph paper. Joining these points we get a line $PQ$.
Thus, $PQ$ is the required graph of $x + y =100$.
Standard 9
Mathematics
