The document Long Answer Type Questions- Linear Equations in Two Variables Class 9 Notes | EduRev is a part of the Class 9 Course Class 9 Mathematics by Full Circle.

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**Question 1. The following observed values of x and y are thought to satisfy a linear equation.**

**Draw the graph using the values of x and y as given in the above table.At what points the graph of the linear equation cuts the x-axis?**

The graph AB, cuts the x-axis at the point C (3, 0) and the y-axis at the point D (0, 2).**Question 2. The taxi fare in a town is ****â‚¹****10 for the first kilometre and ****â‚¹**** 6 per km for the subsequent distance. Taking the distance as â€˜xâ€™ km and total fare as ****â‚¹****y, write a linear equation for this information, what will be the total fare for 15 km? Solution:**

âˆµ Total distance is x km.

Total fare = â‚¹y

âˆ´ x = 1 + (x â€“ 1) = First km + Subsequent distance

Since, fare the first km = â‚¹10

âˆ´ Fare for the remaining distance = â‚¹6 x (x â€“ 1) = â‚¹6x â€“ â‚¹6

â‡’ Total fare = â‚¹10 + â‚¹6x â€“ â‚¹6

= â‚¹4 + â‚¹6x

âˆ´ y = 4 + 6x

â‡’ y â€“ 6x = 4

â‡’ 6x â€“ y + 4 = 0

Which is the required equation.

Now, total fare for 15 km:

6 x 15 â€“ y + 4 = 0 [Substituting x = 15]

â‡’ 90 â€“ y + 4 = 0

â‡’ 94 â€“ y = 0

â‡’ y = 94

âˆ´ Total fare = â‚¹94.**Question 3. Draw the graph of the equation x â€“ y = 4. From the graph, find the coordinates of the point when the graph line meets the x-axis.****Solution:** We have x â€“ y = 4 or y = x â€“ 4

When x = 0, then y = 0 â€“ 4 = â€“4

When x = 1, then y = 1 â€“ 4 = â€“3

When x = â€“1, then y = â€“ 1 â€“ 4 = â€“ 5

We get the following table of values of x and y.

x | 0 | 1 | -1 |

y | -4 | -3 | -5 |

(x, y) | (0, â€“4) | (1, â€“3) | (â€“1, â€“5) |

âˆ´ We have the ordered pairs of solution for x â€“ y = 4 as (0, â€“4), (1, â€“3) and (â€“1, â€“5).

Now, plotting the points (0, â€“4), (1, â€“3) and (â€“1, â€“5) and then joining them, we get the following graph of x â€“ y = 4.

From the graph, we find that the graph line meets the x-axis at (4, 0).

**Question 4. Draw the graph x + 2y = 6 and from the graph, find the value of x when y = â€“ 3.****Solution: We have: x + 2y = 6**

â‡’

When x = 0, then

When x = 2, then

When x = 4, then ** **

We get the following table of values of x and y.

x | 0 | 2 | 4 |

y | 3 | 2 | 1 |

(x, y) | (0, 3) | (2, 2) | (4, 1) |

Plotting the ordered pairs (0, 3), (2, 2) and (4, 1) and then joining them, we get the graph of x + 2y = 6 as shown below:

From the graph, we find that for y = â€“ 3, the value of x = 12.