Draw the graphs of the equations 5x – y = 5 and 3x – y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y-axis
Solution:
The representation of a linear equation on a graph is called graphing linear equations.
5x - y = 5
⇒ y = 5x - 5
The solution table will be as follows.
|
x: |
0 |
2 |
|
y: |
- 5 |
5 |
3x - y = 3
⇒ y = 3x - 3
The solution table will be as follows.
|
x: |
0 |
2 |
|
y: |
- 3 |
3 |
The graphical representation of these lines will be as follows.
It can be observed that the required triangle is ABC formed by these lines and the y-axis. The coordinates of vertices are A (1, 0), B (0, - 3), C (0, - 5) .
☛ Check: NCERT Solutions Class 10 Maths Chapter 3
Video Solution:
Draw the graphs of the equations 5x – y = 5 and 3x – y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and the y axis
Class 10 Maths NCERT Solutions Chapter 3 Exercise 3.7 Question 6
Summary:
The co-ordinates of the vertices of the triangle formed by the equations 5x - y = 5 and 3x - y = 3 and the y axis are A (1, 0), B (0, - 3), C (0, - 5).
☛ Related Questions:
- One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital? [From the Bijaganita of Bhaskara II] [Hint: x +100 = 2 ( y -100), y +10 = 6 (x -10)]
- A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.
- The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.
- In △ABC, ∠C = 3∠B = 2(∠A + ∠B) . Find the three angles.