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NCERT exemplar Class 9 Maths solutions chapter 4 provide students with detailed answers for the chapter 4 Linear Equation in two variables. These NCERT Solutions are important as the concepts used here will be applied in mathematics courses of higher Classes. NCERT exemplar solutions for Class 9 Maths chapter 4 gives a good number of practice questions.
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These NCERT exemplar Class 9 Maths solutions chapter 4 are also useful for competitive exams like JEE Main, advanced and NEET and other state and class 9 CBSE syllabus. The Class 9 Maths NCERT exemplar chapter 4 solutions are useful to solve Class 9 Physics problems.
Question:1
The linear equation has
(A) A unique solution
(B) Two solutions
(C) Infinitely many sol
Question:2
The equation 2x+5y=7 has a unique solution, if x, y are :
(A) Natural numbers
(B) Positive real numbers
(C) Real numbers
(D) Rational numbers
Question:3
If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is
(A) 4
(B) 6
(C) 5
(D) 2
Question:4
Any solution of the linear equation 2x + 0y + 9 = 0 in two variables is of the form
(A)
(B)
(C)
(D) (–9, 0)
Question:5
The graph of the linear equation 2x + 3y = 6 cuts the y-axis at the point
(A) (2, 0)
(B) (0, 3)
(C) (3, 0)
(D) (0, 2)
Question:6
The equation x = 7, in two variables, can be written as
(A) 1.x + 1.y = 7
(B) 1.x + 0.y = 7
(C) 0.x + 1.y = 7
(D) 0.x + 0.y = 7
Question:7
Any point on the x-axis is of the form
(A) (x, y)
(B) (0, y)
(C) (x, 0)
(D) (x, x)
Question:8
Any point on the line y = x is of the form
(A) (a, a)
(B) (0, a)
(C) (a, 0)
(D) (a, – a)
Question:9
The equation of x-axis is of the form
(A) x = 0
(B) y = 0
(C) x + y = 0
(D) x = y
Question:10
The graph of y = 6 is a line
(A) parallel to x-axis at a distance 6 units from the origin
(B) parallel to y-axis at a distance 6 units from the origin
(C) making an intercept 6 on the x-axis.
(D) making an intercept 6 on both the axes.
Question:11
x = 5, y = 2 is a solution of the linear equation
(A) x + 2 y = 7
(B) 5x + 2y = 7
(C) x + y = 7
(D) 5 x + y = 7
Question:12
If a linear equation has solutions (–2, 2), (0, 0) and (2, – 2), then it is of the form
(A) y – x = 0
(B) x + y = 0
(C) –2x + y = 0
(D) –x + 2y = 0
Question:13
The positive solutions of the equation ax + by + c = 0 always lie in the
(A) 1st quadrant
(B) 2nd quadrant
(C) 3rd quadrant
(D) 4th quadrant
Question:14
The graph of the linear equation 2x + 3y = 6 is a line which meets the x-axis at the point:
(A) (0, 2)
(B) (2, 0)
(C) (3, 0)
(D) (0, 3)
x | 0 | 3 |
y | 2 | 0 |
Question:15
The graph of the linear equation y = x passes through the point
(A)
(B)
(C) (1, 1)
(D)
Question:16
If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation :
(A) Changes
(B) Remains the same
(C) Changes in case of multiplication only
(D) Changes in case of division only
Question:17
How many linear equations in x and y can be satisfied by x = 1 and y = 2?
(A) Only one
(B) Two
(C) Infinitely many
(D) Three
Question:18
The point of the form (a, a) always lies on:
(A) x-axis
(B) y-axis
(C) On the line y = x
(D) On the line x + y = 0
Question:19
The point of the form (a, – a) always lies on the line
(A) x = a
(B) y = – a
(C) y = x
(D) x + y = 0
Question:1
Answer:Question:2
Answer:x | 0 | 7 | 1 |
y | 0 | 3 |
Question:3
Answer:Question:4
Answer:Question:5
x | 0 | 1 | 2 | 3 | 4 |
y | 2 | 3 | 4 | -5 | 6 |
x | 0 | 1 | 2 | 3 | 4 |
y | 2 | 3 | 4 | -5 | 6 |
Question:6
Answer:Question:7
Answer:Question:1
Answer:
First of all the us plot the graph of linear equation y = x and y = –xQuestion:2
Answer:Question:3
Answer:
We know that the straight line which is parallel to the x-axis is on the y-intercept, i.e. there is no x-intercept on it.Question:4
Answer:
It is given that sum of the ordinates is 10 unitsx | 1 | 2 | 3 |
y | 9 | 8 | 7 |
Question:5
Write the linear equation such that each point on its graph has an ordinate 3 times its abscissa.
Answer:
It is given that the ordinate is 3 times its abscissa.x | 0 | 1 | 2 |
y | 0 | 3 | 6 |
Question:6
If the point (3, 4) lies on the graph of 3y = ax + 7, then find the value of a.
Answer:Question:7
How many solution(s) of the equation 2x + 1 = x – 3 are there on the number line?
How many solution(s) of the equation 2x + 1 = x – 3 are there on the Cartesian plane?
Question:8
Find the solution of the linear equation x + 2y = 8 which represents a point on x-axis.
Find the solution of the linear equation x + 2y = 8 which represents a point on y-axis.
Question:9
For what value of c, the linear equation 2x + cy = 8 has equal values of x and y for its solution.
Answer:
Answer:Question:10
Answer:Question:1
Answer:
The given linear equation is y = 9x – 7 and the points are A(1, 2), B(–1, –16) and C(0, –7)Question:2
x | 6 | -6 |
y | -2 | 6 |
Answer:
Let the linear equation is y = mx + c … (i), and it satisfies the points (6, –2), (–6, 6)Question:3
Answer:
The given equation is 3x + 4y = 6 …(i)Question:4
The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation If the temperature is 86°F, what is the temperature in Celsius?
The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation .If the temperature is , what is the temperature in Fahrenheit (F)?
The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation .If the temperature is what is the temperature in Fahrenheit and if the temperature is , what is the temperature in Celsius?
The linear equation that converts Fahrenheit (F) to Celsius (C) is given by the relation .What is the numerical value of the temperature which is same in both the scales?
Question:5
Answer:
Given that,
Put the value of x = in equation (1), we get
Given that,
Put
in equation (1)
we get
790 – 160 = 9x – 2457630 + 2457 = 9x
3087 = 9x
343 = x
Hence answer is 343K
Question:6
The force exerted to pull a cart is directly proportional to the acceleration produced in the body. Express the statement as a linear equation of two variables and draw the graph of the same by taking the constant mass equal to 6 kg. Read from the graph, the force required when the acceleration produced is 5 m/sec^{2}.
The force exerted to pull a cart is directly proportional to the acceleration produced in the body. Express the statement as a linear equation of two variables and draw the graph of the same by taking the constant mass equal to 6 kg. Read from the graph, the force required when the acceleration produced is 6 m/sec^{2}.
Answer:
It is given that force is directly proportional to accelerationF | 6 | 12 |
a | 1 | 2 |
F | 6 | 12 |
a | 1 | 2 |
The major pointers of this chapter covered in the NCERT exemplar Class 9 Maths solutions chapter 4 are mentioned below:
◊ Making two-variable linear equations for any given situation or statement.
◊ We will learn to solve these linear equations to find out the values of variables.
◊ NCERT exemplar Class 9 Maths solutions chapter 4 include methods to solve these linear equations to determine the values of variables.
◊ These linear equations can be drawn on a Cartesian plane as straight lines.
◊ We can find out the values of variables by geometric representations of these equations.
◊ We learn about linear equations representing lines parallel to X-axis or Y-axis and the line passing through the origin.
These Class 9 Maths NCERT exemplar chapter 4 solutions will help the students grasp the basics of linear equations in two variables. It gives two relations between Binomial of two variables of a single degree. With the help of those two equations, we have to determine the values of two variables individually. The chapter on Linear Equations in Two Variables can be studied and practiced using these NCERT exemplar Class 9 Maths chapter 4 solutions Linear Equations in Two Variables and will be enough to solve other books such as A textbook of Mathematics by Monica Kapoor, NCERT Class 9 Maths, RD Sharma Class 10 Maths, RS Aggarwal Class 9 Maths et cetera. NCERT exemplar Class 9 Maths solutions chapter 4 pdf download is a free-to-use feature. The solutions can be downloaded using any tools that are available to convert the page to pdf.
Chapter No. | Chapter Name |
Chapter 1 | |
Chapter 2 | |
Chapter 3 | |
Chapter 4 | |
Chapter 5 | |
Chapter 6 | |
Chapter 7 | |
Chapter 8 | |
Chapter 9 | |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | |
Chapter 13 | |
Chapter 14 | |
Chapter 15 |
No, we cannot solve any two equations of two variables all the time, however, yes, if these two equations are linear, we can always solve them provided they have a solution.
No, two equations written in the linear form of two variables can have zero solution, infinite solution and precisely one unique solution.
Yes, we can solve linear equations of three variables. However, the same method we use in linear equations of two variables will not be used as later we will study solving these equations using a matrix method.
Generally 8-10% of the marks of the final paper account for Linear equation in two variables. The class 9 maths NCERT exemplar solutions of chapter 4 are equipped with the detailed solutions to ace the final examinations.
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Application Date:09 September,2024 - 14 November,2024
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