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NCERT Solutions for class 10 maths ex 3.2 Pair of Linear Equations in two variables is discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. This ex 3.2 class 10 deals with the graphical and algebraic representations of linear equations in two variables and their different type of solutions such as a unique solution, no solutions or infinitely many solutions, using the five methods namely the Graphical method, substitution method, cross Multiplication method, elimination method and determinant method.
These class 10 maths ex 3.2 solutions are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.
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Pair of Linear Equations in Two Variables Class 10 Chapter 3 Exercise: 3.2
Q1 Form the pair of linear equations in the following problems and find their solutions graphically.
Answer:
Let the number of boys is x and the number of girls is y.
Now, According to the question,
Total number of students in the class = 10, i.e.
And
the number of girls is 4 more than the number of boys,i.e.
Different points (x, y) for equation (1)
X | 5 | 6 | 4 |
Y | 5 | 4 | 6 |
Different points (x,y) satisfying (2)
X | 5 | 6 | 7 |
y | 1 | 2 | 3 |
Graph,
As we can see from the graph, both lines intersect at the point (7,3). that is x= 7 and y = 3 which means the number of boys in the class is 7 and the number of girls in the class is 3.
Q1 Form the pair of linear equations in the following problems and find their solutions graphically.
Answer:
Let x be the price of 1 pencil and y be the price of 1 pen,
Now, According to the question
And
Now, the points (x,y), that satisfies the equation (1) are
X | 3 | -4 | 10 |
Y | 5 | 10 | 0 |
And, the points(x,y) that satisfies the equation (2) are
X | 3 | 8 | -2 |
Y | 5 | -2 | 12 |
The Graph,
As we can see from the Graph, both line intersects at point (3,5) that is, x = 3 and y = 5 which means cost of 1 pencil is 3 and the cost of 1 pen is 5.
Answer:
Give, Equations,
Comparing these equations with , we get
As we can see
It means that both lines intersect at exactly one point.
Answer:
Given, Equations,
Comparing these equations with , we get
As we can see
It means that both lines are coincident.
Q2 On comparing the ratios , and , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident: (iii)
Answer:
Give, Equations,
Comparing these equations with , we get
As we can see
It means that both lines are parallel to each other.
Answer:
Give, Equations,
Comparing these equations with , we get
As we can see
It means the given equations have exactly one solution and thus pair of linear equations is consistent.
Answer:
Given, Equations,
Comparing these equations with , we get
As we can see
It means the given equations have no solution and thus pair of linear equations is inconsistent.
Answer:
Given, Equations,
Comparing these equations with , we get
As we can see
It means the given equations have exactly one solution and thus pair of linear equations is consistent.
Answer:
Given, Equations,
Comparing these equations with , we get
As we can see
It means the given equations have an infinite number of solutions and thus pair of linear equations is consistent.
Answer:
Given, Equations,
Comparing these equations with , we get
As we can see
It means the given equations have an infinite number of solutions and thus pair of linear equations is consistent.
Answer:
Given, Equations,
Comparing these equations with , we get
As we can see
It means the given equations have an infinite number of solutions and thus pair of linear equations is consistent.
The points (x,y) which satisfies in both equations are
X | 1 | 3 | 5 |
Y | 4 | 2 | 0 |
Answer:
Given, Equations,
Comparing these equations with , we get
As we can see
It means the given equations have no solution and thus pair of linear equations is inconsistent.
Answer:
Given, Equations,
Comparing these equations with , we get
As we can see
It means the given equations have exactly one solution and thus pair of linear equations is consistent.
Now The points(x, y) satisfying the equation are,
X | 0 | 2 | 3 |
Y | 6 | 2 | 0 |
And The points(x,y) satisfying the equation are,
X | 0 | 1 | 2 |
Y | -2 | 0 | 2 |
GRAPH:
As we can see both lines intersects at point (2,2) and hence the solution of both equations is x = 2 and y = 2.
Answer:
Given, Equations,
Comparing these equations with , we get
As we can see
It means the given equations have no solution and thus pair of linear equations is inconsistent.
Answer:
Let be the length of the rectangular garden and be the width.
Now, According to the question, the length is 4 m more than its width.i.e.
Also Given Half Parameter of the rectangle = 36 i.e.
Now, as we have two equations, on adding both equations, we get,
Putting this in equation (1),
Hence Length and width of the rectangle are 20m and 16 respectively.
Answer:
Given the equation,
As we know that the condition for the intersection of lines , is ,
So Any line with this condition can be
Here,
As
the line satisfies the given condition.
Answer:
Given the equation,
As we know that the condition for the lines , for being parallel is,
So Any line with this condition can be
Here,
As
the line satisfies the given condition.
Answer:
Given the equation,
As we know that the condition for the coincidence of the lines , is,
So any line with this condition can be
Here,
As
the line satisfies the given condition.
Answer:
Given, two equations,
And
The points (x,y) satisfying (1) are
X | 0 | 3 | 6 |
Y | 1 | 4 | 7 |
And The points(x,y) satisfying (2) are,
X | 0 | 2 | 4 |
Y | 6 | 3 | 0 |
GRAPH:
As we can see from the graph that both lines intersect at the point (2,3), And the vertices of the Triangle are ( -1,0), (2,3) and (4,0). The area of the triangle is shaded with a green colour.
The emphasis of NCERT solutions for Class 10 Maths exercise 3.2 was on graphical representations of linear equations in two variables, types of solutions, and associated graphs. Two systems of equations can be parallel at times. They have no solution in such situations. In rare situations, the two systems of equations may coincide, resulting in an infinite number of solutions for the given system. If the two systems of equations overlap, the given system is said to be consistent because it has a unique solution. NCERT solutions for Class 10 Maths exercise 3.2 was on the graphical depiction of the system of equations. NCERT syllabus Exercise 3.2 Class 10 Maths contains all three questions relating to the graphical depiction.Also students can get access of Pair of linear equations in two variables notes to revise all the concepts discussed in this chapter.
Also see-
The concepts related to linear equation is discussed in ex 3.2 class 10. Practice the problems discussed in this exercise to command the concepts. For this question, because of the term xy is of degree 2, xy - 9 = 3 is not a linear equation in two variables.
To understand the concepts of quadrants go through the problems discussed in class 10 maths ex 3.2. In a graph, there are four quadrants. a point can be represent in in a plain using the (x, y) coordinates.
To get in depth understanding of related concepts practice problems enumerated in the class 10 ex 3.2. as per these concepts, when two lines are in a plane, there are three alternative solutions. They really are.
In Class 10th Maths chapter 3 exercise 3.2, there are seven questions based on the notion of graphical representation of a system of equations.
If the equations are consistent and dependent, there are no solutions to linear equations in two variables.
You can go through the 10th class maths exercise 3.2 answers to get deeper understanding of the concepts related to equations are consistent and dependent. The requirement for linear equations in two variables is:
a1/a2 = b1/b2 = c1/c2
The basic strategy to represent the linear equations on the graph and determine the point of intersection is the graphical method of solution of a pair of linear equations.
Hello Aspirant, Hope your doing great, your question was incomplete and regarding what exam your asking.
Yes, scoring above 80% in ICSE Class 10 exams typically meets the requirements to get into the Commerce stream in Class 11th under the CBSE board . Admission criteria can vary between schools, so it is advisable to check the specific requirements of the intended CBSE school. Generally, a good academic record with a score above 80% in ICSE 10th result is considered strong for such transitions.
hello Zaid,
Yes, you can apply for 12th grade as a private candidate .You will need to follow the registration process and fulfill the eligibility criteria set by CBSE for private candidates.If you haven't given the 11th grade exam ,you would be able to appear for the 12th exam directly without having passed 11th grade. you will need to give certain tests in the school you are getting addmission to prove your eligibilty.
best of luck!
According to cbse norms candidates who have completed class 10th, class 11th, have a gap year or have failed class 12th can appear for admission in 12th class.for admission in cbse board you need to clear your 11th class first and you must have studied from CBSE board or any other recognized and equivalent board/school.
You are not eligible for cbse board but you can still do 12th from nios which allow candidates to take admission in 12th class as a private student without completing 11th.
Yes, you can definitely apply for diploma courses after passing 10th CBSE. In fact, there are many diploma programs designed specifically for students who have completed their 10th grade.
Generally, passing 10th CBSE with a minimum percentage (often 50%) is the basic eligibility for diploma courses. Some institutes might have specific subject requirements depending on the diploma specialization.
There is a wide range of diploma courses available in various fields like engineering (e.g., mechanical, civil, computer science), computer applications, animation, fashion design, hospitality management, and many more.
You can pursue diplomas at various institutions like:
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