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 xaxis?
Solution. Plotting the points (6, –2) and (–6, 6) and joining them we get the graph AB which is the required graph.
The graph AB cuts the xaxis at point C (3, 0) and the yaxis at point D (0, 2).
Question 2. The taxi fare in a town is ₹10 for the first kilometre and ₹ 6 per km for the subsequent distance. Taking the distance as ‘x’ km and total fare as ₹y, write a linear equation for this information, what will be the total fare for 15 km?
Solution:
∵ Total distance is x km.
Total fare = ₹y
∴ x = 1 + (x – 1) = First km + Subsequent distance
Since, fare the first km = ₹10
∴ Fare for the remaining distance = ₹6 x (x – 1) = ₹6x – ₹6
⇒ Total fare = ₹10 + ₹6x – ₹6
= ₹4 + ₹6x
∴ y = 4 + 6x
⇒ y – 6x = 4
⇒ 6x – y + 4 = 0
Which is the required equation.
Now, total fare for 15 km:
6 x 15 – y + 4 = 0 [Substituting x = 15]
⇒ 90 – y + 4 = 0
⇒ 94 – y = 0
⇒ y = 94
∴ Total fare = ₹94.
Question 3. Draw the graph of the equation x – y = 4. From the graph, find the coordinates of the point when the graph line meets the xaxis.
Solution: We have x – y = 4 or y = x – 4
When x = 0, then y = 0 – 4 = –4
When x = 1, then y = 1 – 4 = –3
When x = –1, then y = – 1 – 4 = – 5
We get the following table of values of x and y.
x  0  1  1 
y  4  3  5 
(x, y)  (0, –4)  (1, –3)  (–1, –5) 
∴ We have the ordered pairs of solution for x – y = 4 as (0, –4), (1, –3) and (–1, –5).
Now, plotting the points (0, –4), (1, –3) and (–1, –5) and then joining them, we get the following graph of x – y = 4.
From the graph, we find that the graph line meets the xaxis at (4, 0).
Question 4. Draw the graph x + 2y = 6 and from the graph, find the value of x when y = – 3.
Solution: We have: x + 2y = 6
⇒
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 = – 3, the value of x = 12.
1. What are linear equations in two variables? 
2. How do you solve a system of linear equations in two variables? 
3. What is the importance of linear equations in two variables? 
4. Can a linear equation in two variables have infinitely many solutions? 
5. How can linear equations in two variables be used to solve word problems? 
62 videos426 docs102 tests

62 videos426 docs102 tests
