Important Questions Class 9 Maths Chapter 13 Two Variables, One Line
Important Questions Class 9 Maths Chapter 13 Two Variables, One Line
Two Variables, One Line is Chapter 13 of the Class 9 Maths textbook Ganita Manjari. The chapter introduces linear equations in two variables, written in the form ax + by + c = 0. You learn that such an equation has many solutions, how to find and check solutions, how to draw the graph of the equation, and why every point on the line is a solution.
This page gives 12 important questions from Two Variables, One Line with step-by-step answers by Extramarks experts. The set includes writing equations from word problems such as taxi fare and distance-time, finding solutions, checking whether a point lies on a line, finding the value of an unknown constant, and drawing graphs. Practise the graph questions with a ruler and graph paper.
Q1. Write a linear equation in two variables for which x = 4 and y = –2 is a solution. Justify your answer.
Answer:
There are infinitely many such equations possible.
Q2. Find any three distinct solutions for the linear equation 2x – y = –2 and demonstrate how you verified them.
Answer: Three distinct solutions for the linear equation 2x – y = –2 are (0, 2), (1, 4) and (–1, 0).
Verification:
1. For (0, 2): 2(0) – 2 = 0 – 2 = –2. (LHS = RHS)
2. For (1, 4): 2(1) – 4 = 2 – 4 = –2. (LHS = RHS)
3. For (–1, 0): 2(–1) – 0 = –2 – 0 = –2. (LHS = RHS)
Since the LHS equals the RHS for all three pairs, they are correct solutions. Note that there are infinitely many solutions, and any three valid pairs would be correct.
Q3. Represent the equation 5x + 18 = 0 in one variable and two variables form. Geometrically represent the solutions of above equation on number line and Cartesian plane. Check whether the representing line (in Cartesian plane) is parallel to any axis.
Answer:
Q4.
given by:
Graph the equation and determine the cost of painting walls of a cubical room with side 4 m.
Answer: Consider the given relation between cost and area.
To draw the line, we need two solutions of the given equation by substituting two values of A. For A = 0,
The table for the values of A and C is shown as:
Now, plot the two points (0, 1500) and (20, 2750). Join these points to get the line as shown. For A = 64,
The required cost is 5500 (in rupees).
Q5. Check whether the following equation represents a linear equation in two variables.
If yes, then compare it with the standard form ax + by + c = 0 and find the value of a + b + c. Is this value an irrational number?
Answer:
In the above equation, variables are x and y with exponent 1. So, it's a linear equation in two variables. To obtain a, b and c, we write the given equation in the form ax + by + c = 0.
= 1 (Rational number)
Q6.
Answer:
Q7.
Answer: Solutions of equation, x = – 2 Writing the above equation in the form, ax + by + c = 0 as x + 0 × y + 2 = 0 The solutions obtained by substituting random values of y in the above equation.
Solutions of equation, y = 4 Writing the above equation in the form, ax + by + c = 0 as 0 × x + y – 4 = 0 The solutions obtained by substituting the random values of x in the above equation.
Plotting the solutions obtained from both the equations we get,
From the above representation on the cartesian plane, the coordinates of a point that is a solution to both the equation is (– 2, 4).
Q8.
Answer:
Q9. The taxi fare in a city is as follows:
For the first kilometre, the fare is ₹ 8 and for the subsequent distance, it is ₹ 5 per km. Taking the distance covered as x km and total fare as ₹ y, write a linear equation for this information and write the equation in standard form.
Answer:
Q10. If the point (4, 3) lies on the graph of the equation 3x – ay = 6, find whether (–2, –6) also lies on the same graph.
Answer:
Q11. At what point does the graph of the linear equation 2x + 3y = 9 meets a line which is parallel to the y-axis, at a distance of 4 units from the origin and on the right of the y-axis.
Answer: Given linear equation is: 2x + 3y = 9 Equation of line which is parallel to y-axis and 4 units right from origin is x = 4. So, for the point of intersection for both the lines, we have 2(4) + 3y = 9, 8 + 3y = 9, y = 1/3
Therefore, the required point is
Q12. If the point (–1, –5) lies on the graphs of 3x = ay + 7 and y = bx + 7, find the value of a and b.
Answer: Point (–1, –5) lies on the graphs of 3x = ay + 7, so, 3(–1) = a(–5)+7 –3 = –5a+7 –10 = –5a a = 2 Point (–1, –5) lies on the graphs of y = bx + 7, so, –5 = b(–1) + 7 –5 = –b + 7 b = 12
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Q.1 The internal measurements of a cuboidal room are 10 m × 4 m × 6 m. Find the cost of white washing of the walls at the rate of 5 per square metre.
Marks:3
Ans
Area of four walls of room = 2(l + b)h
= 2—(10 + 4)—6
= 168 m2
Rate of white washing = 5 per m2
So,
the total cost of white washing
= 5—168
= 840
Q.2 How many bricks will be required for a wall 8 m long, 6 m high and 22.5 cm thick if each brick measures 25 cm x 11.25 cm x 6 cm
Marks:3
Ans
Q.3 Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of sum of the surface areas of the three cubes.
Marks:3
Ans
Q.4 The radius and slant height of a cone are in the ratio 4:7. If its curved surface area is 792 sq cm, find its radius.
Marks:3
Ans
Q.5 The diameter of a sphere is decreased by 50%. By what percent will its curved surface area decrease
Marks:3
Ans
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 There are 15 chapters in Class 9 Mathematics. The list is given below:
- Chapter 1- Number System
- Chapter 2 –Polynomials
- Chapter 3 – Coordinate Geometry
- Chapter 4 –Linear Equations In Two Variables
- Chapter 5 – Introduction To Euclid’s Geometry
- Chapter 6 – Lines And Angles
- Chapter 7 –Triangles
- Chapter 8 – Quadrilaterals
- Chapter 9 –Areas Of Parallelograms And Triangles
- Chapter 10 – Circles
- Chapter 11- Constructions
- Chapter 12- Heron’s Formula
- Chapter 13-Surface Area And Volumes
- Chapter 14- Statistics
- Chapter 15- Probability