The document Notes | EduRev is a part of the Class 9 Course Mathematics (Maths) Class 9.

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**Worksheet (Part - 1)**

**1.** Write each of the following as an equation in two variables:

(i) x = â€“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 â€“ 9 = âˆš3 y

(iii) 4 = 5x â€“ 8y

(iv) y = 2x**ANSWERS****1. **(i) x + (0)y + 3 = 0

(ii) (0)x + y = 2

(iii) 2x + (0)y â€“ 3 = 0

(iv) (0)x + 2y â€“ 5 = 0

**2. **(i) 2x + 3y â€“ 3.47 = 0; a = 2, b = 3 and c = â€“3.47

(ii) x â€“ âˆš3y â€“ 9 = 0; a = 1, b = - âˆš3 and c = â€“9

(iii) â€“5x + 8y + 4 = 0; a = â€“5, b = 8 and c = 4

(iv) â€“2x + y + 0 = 0; a = â€“2, b = 1 and c = 0

**Worksheet (Part - 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 â€“ 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 (Part - 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 â€“ y = 0

(iii) 2x = y

(iv) y = 2x + 1

**Fig. (b) **

(i) x + y = 0

(ii) x â€“ y = 0

(iii) y = 2x + 4

(iv) y = x â€“ 4

**Fig. (c) **

(i) x + y = 0

(ii) x â€“ y = 0

(iii) y = 2x + 1

(iv) y = 2x â€“ 4

**Fig. (d) **

(i) x + y = 0

(ii) x â€“ y = 0

(iii) 2x + y = â€“4

(iv) 2x + y = 4**ANSWERS**

**1.** x + y = 3

**3.** y = 3x

**4. **(a) x â€“ y = 0

(b) y = 2x + 4

(c) y = 2x â€“ 4

(d) 2x + y = â€“4**Worksheet (Part - 4)**

**1.** Give the geometric representation of x = 7 as an equation

(i) in one variable

(ii) in two variables**2.** Solve the equation 3x + 1 = 2x â€“ 1 and represent the solution(s) on:

(i) a number line

(ii) the cartesian plane**Hint:** (ii) 3x + 1 = 2x â€“ 1 â‡’ 3x â€“ 2x = â€“1 â€“ 1 â‡’ x = â€“2 â‡’ x + 0y = â€“2**Worksheet (Part - 5)**

**1.** Which of the following is not a linear equation in two variables?

(i) px + qy + c = 0

(ii) ax^{2} + bx + c = 0

(iii) 3x + 2y = 5**2.** One of the solutions of the linear equation 4x â€“ 3y + 6 = 0 is

(i) (3, 2)

(ii) (â€“3, 2)

(iii) (â€“3, â€“2)**3.** lx + my + c = 0 is a linear equation in x and y. For which of the following, the ordered pair (p, q) satisfies it:

(i) lp + mq + c = 0

(ii) y = 0

(iii) x + y = 0

(iv) x = y**4.** What is the equation of x-axis?

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

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

**7.** How many solutions does 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 = â€“1, y = 1?

**16.** The point (m, m) always lies on which of the following lines?

x â€“ 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 = â€“ x passes?

(i) (1, 1)

(ii) (0, 1)

(iii)

(â€“1, 1)

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

**20.** On which of the following equations, the point of the form (m, â€“m) lies?

(i) x = â€“m

(ii) x + y = 0

(iii) y = x

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

**22. **Which equationâ€™s graph is at a distance 3 units to the left of y-axis? x = 3; x = â€“3; or y = x

**23. **The graph of which of the following equations passes through the origin?

(i) y = 2x + c

(ii) y = 2x â€“ 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.** ax^{2} + bx + c = 0

**2.** â€“3, â€“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 â€“ y = 0

**17. **infinitely many equations in x and y 18. (â€“1, 1)

**19. **

**20. **x + y = 0

**21. **neither x-axis nor y-axis

**22.** x = â€“3

**23.** y = 2x

**24.** Natural numbers

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