# Ex.4.3 Q7 Linear Equations in Two Variables Solution - NCERT Maths Class 9

## Question

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.

## Text Solution

**What is known?**

Yamini and Fatima together contributed \(₹\, 100 \)

**What is Unknown?**

Yamini and Fatima contributions and graph for the same.

**Reasoning:**

We can let Yamini and Fatima contributions as \(₹\) \(x\) and \(₹\) \(y\) and form linear equation. Then find \(x\) and \(y\) value to draw graph.

**Steps:**

- 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 \(\rm = ₹\, 100\)

Therefore, \(x + y = 100\)

On transposing, we get \(y = 100 \,– x\)

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

Let us consider this as,

\(y = 100\, – x \quad \dots \text{ Equation } (1)\)

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 \(y\):

\(x\) | \(0\) | \(50\) | \(100\) |

\(y\) | \(100\) | \(50 \) | \(0\) |

By Plotting the points \((0, 100), (100, 0)\) and \((50, 50)\) on the graph paper and drawing a line joining them, we obtain the required graph.

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

Here, variable \(x\) 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 \(1\,\rm st\) quadrant are considered.