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# Long Answer Type Questions- Linear Equations in Two Variables Class 9 Notes | EduRev

## Class 9 Mathematics by Full Circle

Created by: Full Circle

## Class 9 : Long Answer Type Questions- Linear Equations in Two Variables Class 9 Notes | EduRev

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.
All you need of Class 9 at this link: Class 9

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?

Solution. Plotting the points (6, â€“2) and (â€“6, 6) and joining them we get the graph AB which is the required graph.

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‚¹10 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‚¹y, 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.

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