The equation of the x-axis is y = 0 and 2x + 3y = 5 is the linear equation in two variables listed, so this Class 9 sheet opens with the axes equation and the two-variable form. Infinitely many and a (0, 1) point follow in the key.
Key Takeaways
The x-axis has equation y = 0 (Q1).
2x + 3y = 5 is a linear equation in two variables (Q2).
Q4 records infinitely many as the number of solutions.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.The equation of the x-axis is
(a) x = 0(b) y = 0(c) x + y = 0(d) x - y = 0
2.Which of the following is a linear equation in two variables?
(a) 2x + 3y = 5(b) x² + y = 1(c) xy = 6(d) x + 1 = 2
3.For the equation 2x + y = 6, the value of y when x = 1 is
(a) 4(b) 5(c) 6(d) 8
4.The number of solutions of the linear equation 3x + 4y = 12 is
(a) One(b) Two(c) Infinitely many(d) No solution
5.Which point lies on the line y = 2x + 1?
(a) (0, 1)(b) (1, 1)(c) (2, 2)(d) (3, 6)
6.The equation y = 3 written in the form ax + by + c = 0 is
(a) x + 0y + 3 = 0(b) 0x + y - 3 = 0(c) 0x + y + 3 = 0(d) x + y - 3 = 0
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Write the equation 2x - 3y = 6 in the form ax + by + c = 0 and state the values of a, b and c.
8.Check whether (0, 2) is a solution of the equation x + y = 2.
9.Express y in terms of x in the equation x - 2y = 4.
10.Find two solutions of the equation 2x + y = 8.
11.Does the point (3, 1) lie on the line 3x - y = 8? Justify.
12.Write the linear equation for the statement: The cost of a notebook is twice the cost of a pen. Take notebook as y and pen as x.
13.The graph of the equation x = -3 is a line parallel to which axis?
14.Find the x-coordinate of the point where the line 2x + y = 6 meets the x-axis.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.The cost of a book is ₹25 more than twice the cost of a pen. Form a linear equation in two variables, taking the cost of the pen as x and the cost of the book as y.
16.The sum of two numbers is 35. Form a linear equation in two variables, taking the numbers as x and y.
17.Ramesh's father's age is 4 years more than three times Ramesh's age. Form a linear equation, taking Ramesh's age as x and his father's age as y.
18.A taxi charges ₹20 for the first kilometre and ₹12 for each additional kilometre. Express the total fare y for a journey of x km as a linear equation.
19.The perimeter of a rectangle is 40 cm. If its length is x and its breadth is y, form a linear equation relating x and y.
20.The cost of 2 notebooks and 3 pens is ₹80. Form a linear equation, taking the cost of one notebook as x and the cost of one pen as y.
Answer Key
1. b) y = 0
2. a) 2x + 3y = 5
3. a) 4
4. c) Infinitely many
5. a) (0, 1)
6. b) 0x + y - 3 = 0
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is the equation of the x-axis?
y = 0, option (b) in this worksheet (Q1).
Which is a linear equation in two variables?
2x + 3y = 5, option (a) in this worksheet (Q2).
How many solutions does a linear equation in two variables have?
Infinitely many, option (c) in this worksheet (Q4).
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