Worksheet: Linear Equations in Two Variables - Mathematics (Maths) Class 9

Worksheet- 1

1. Write each of the following as an equation in two variables:
(i) x = –3
(ii)y = 2
(iii) 2x = 3
(iv) 2y = 5

2. Write each of the following equations in the form ax + by + c = 0 and also write the values of a, b and c in each case:
(i) 2x + 3y = 3.47
(ii) x – 9 = √3 y
(iii) 4 = 5x – 8y
(iv) y = 2x

Answers

1. (i) x + (0)y + 3 = 0
(ii) (0)x + y = 2
(iii) 2x + (0)y – 3 = 0
(iv) (0)x + 2y – 5 = 0

2. (i) 2x + 3y – 3.47 = 0; a = 2, b = 3 and c = –3.47
(ii) x – √3y – 9 = 0; a = 1, b = - √3 and c = –9
(iii) –5x + 8y + 4 = 0; a = –5, b = 8 and c = 4
(iv) –2x + y + 0 = 0; a = –2, b = 1 and c = 0

Worksheet- 2

1. (a) Is (3, 2) a solution of 2x + 3y = 12?
(b) Is (1, 4) a solution of 2x + 3y = 12?
(c) Is  a solution of 2x + 3y = 12?
(d) Is  a solution of 2x + 3y = 12?
2. Find four different solutions of the equation x + 2y = 6.

3. Find two solutions for each of the following equations:
(i) 4x + 3y = 12
(ii) 2x + 5y = 0
(iii) x + 3y + 4 = 0
4. Find the value of k such that x = 2 and y = 1 is a solution of the linear equation 2x – ky + 7 = 8

Answers

1. (a)Yes
(b)No
(c)Yes
(d)Yes 

2. (i) (2, 2)
(ii) (0, 3)
(iii) (6, 0)
(iv) (4, 1) 

3. (i) (0, 4) and (3, 0)
(ii) (0, 0) and
(iii)

Worksheet- 3

1. Write a linear equation such that the point (1, 2) lies on its graph. 

2. Draw the graph of x + y = 9. 

3. Force applied on a body is directly proportional to the acceleration produced in the body.
Write an equation to express this situation and plot the graph of the equation. 

4. For each of the graph given in the following figure select the equation whose graph it is from the choices given below:
Fig. (a) 
(i) x + y = 0
(ii) x – y = 0
(iii) 2x = y
(iv) y = 2x + 1 

Fig. (b) 
(i) x + y = 0
(ii) x – y = 0
(iii) y = 2x + 4
(iv) y = x – 4 

Fig. (c) 
(i) x + y = 0
(ii) x – y = 0
(iii) y = 2x + 1
(iv) y = 2x – 4 

Fig. (d) 
(i) x + y = 0
(ii) x – y = 0
(iii) 2x + y = –4
(iv) 2x + y = 4

Answers

1. x + y = 3 

3. y = 3x 

4. (a) x – y = 0
(b) y = 2x + 4
(c) y = 2x – 4
(d) 2x + y = –4

Worksheet- 4

Worksheet- 5

5. What is the equation of the y-axis? 

6. How many solutions do a linear equation in two variables x and y have? 

7. How many solutions do the equation 5x + 2y = 7 can have?

8. Which of the following can be a form of solution of 3x + 0y + 7 = 0 in two variables?

9. What is the form of any point on the line y = x?

10. At which point the linear equation 2x + 3y = 6 cuts the y-axis? 

11. Write the point where the graph of linear equation 2x + 9y = 8 cuts the x-axis.

12. What is the general form of a point on the y-axis?

13. What is the general form of a point on the x-axis?

14. Write the situation of the graph of y = 9 on the cartesian axis. 

15. Write the linear equation whose solution is x = –1, y = 1? 

16. The point (m, m) always lies on which of the following lines?
x – y = 0    or    x + y = 2m 

17. How many linear equations in x and y can have a solution as (x = 1, y = 3)? 

18. Through which of the following points, the graph of y = – x passes?
(i) (1, 1)
(ii) (0, 1)
(iii) (–1, 1)

19. Through which of the following points, the graph of the linear equation 3x – 2y = 0, passes?

20. On which of the following equations, the point of the form (m, –m) lies?
(i) x = –m
(ii) x + y = 0
(iii) y = x 

21. Do the points (2, 0), (–3, 0), (0, 2), (0, –5) lie either on x-axis or y-axis? 

22. Which equation’s graph is at a distance 3 units to the left of y-axis? x = 3; x = –3; or y = x 

23. The graph of which of the following equations passes through the origin?
(i) y = 2x + c
(ii) y = 2x – c
(iii) y = 2x 

24. Fill in the blank: The equation 2x + 5y = 7 has a unique solution if x and y are ......

Answers

1. ax² + bx + c = 0 

2. –3, –2 

3. lp + mq + c = 0 

4. y = 0 

5. x = 0 

6. infinitely many solutions

7. infinitely many solutions

8.

9. (a, a)

10. (0, 2)

11. (4, 0)

12. (0, y)

13. (0, x) 

14. Parallel to x-axis at a distance 9 units from the origin. 

15. x + y = 0 

16. the line x – y = 0 

17. infinitely many equations in x and y 18. (–1, 1)

19. 

20. x + y = 0 

21. neither x-axis nor y-axis 

22. x = –3 

23. y = 2x 

24. Natural numbers