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The exercise explains how to solve a pair of linear equations through graphical methods. The lesson establishes how two linear equations display as straight lines on a Cartesian coordinate system, where their point of intersection reveals the solution. The visualisation enables learners to determine the solution possibilities based on the line behaviour of lines intersecting or being parallel, or coinciding. The process reveals how algebra functions together with geometric principles to solve problems that exist in the real world.
Understandings of two-variable linear equation behaviour in graphical representations are taught in this essential section of the NCERT Solutions for Class 10 Maths. Students who perform exercise gain deeper comprehension about linear equation graphical solutions and system consistency, and how it determines unique versus infinite solutions. The clear presentation of the solutions given in the NCERT Books enables students' understanding of the connection between graphical interpretations and algebraic processes before moving on to complex multisystem topics in higher education.
Answer:
Let the number of boys be x and the number of girls be y.
Now, according to the question,
Total number of students in the class = 10, i.e.
And, given that the number of girls is 4 more than the number of boys it means;
Different points (x, y) satisfying equation (1)
X | 5 | 6 | 4 |
Y | 5 | 4 | 6 |
Different points (x,y) satisfying equation (2)
X | 5 | 6 | 7 |
y | 1 | 2 | 3 |
Graph,
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.
Answer:
Let the price of 1 pencil be x, and y be the price of 1 pen.
Now, according to the question
And
Now, the points (x,y) that satisfy the equation (1) are
X | 3 | -4 | 10 |
Y | 5 | 10 | 0 |
And, the points (x,y) that satisfy the equation (2) are
X | 3 | 8 | -2 |
Y | 5 | -2 | 12 |
The Graph,
From the graph, both lines intersect at point (3,5), that is, x = 3 and y = 5, which means the cost of 1 pencil is 3 and the cost of 1 pen is 5.
Answer:
Given Equations,
Comparing these equations with
It is observed that;
It means that both lines intersect at exactly one point and have a unique solution.
Answer:
Given Equations,
Comparing these equations with
It is observed that;
It means that both lines are coincident and have infinitely many solutions.
Q2 (iii) On comparing the ratios
Answer:
Given Equations,
Comparing these equations with
It is observed that;
It means that both lines are parallel and thus have no solution.
Answer:
Given Equations,
Or,
Comparing these equations with
It is observed that;
It means that the given equations have a unique solution and thus the pair of linear equations is consistent.
Answer:
Given Equations,
Or,
Comparing these equations with
It is observed that;
It means the given equations have no solution, and thus the pair of linear equations is inconsistent.
Answer:
Given Equations,
Or,
Comparing these equations with
It is observed that;
It means the given equations have exactly one solution, and thus the pair of linear equations is consistent.
Answer:
Given Equations,
Or,
Comparing these equations with
It is observed that;
It means the given equations have an infinite number of solutions, and thus a pair of linear equations is consistent.
Answer:
Given Equations,
Or,
Comparing these equations with
It is observed that;
It means the given equations have an infinite number of solutions, and thus a pair of linear equations is consistent.
Answer:
Given Equations,
Comparing these equations with
It is observed that;
It means the given equations have an infinite number of solutions, and thus a pair of linear equations is consistent.
The points (x,y) which satisfy both equations are
X | 1 | 3 | 5 |
Y | 4 | 2 | 0 |
Answer:
Given Equations,
Comparing these equations with
It is observed that:
It means the given equations have no solution, and thus the pair of linear equations is inconsistent.
Answer:
Given Equations,
Comparing these equations with
It is observed that;
It means the given equations have exactly one solution, and thus the pair of linear equations is consistent.
The points(x, y) satisfying the equation
X | 0 | 2 | 3 |
Y | 6 | 2 | 0 |
And The points(x,y) satisfying the equation
X | 0 | 1 | 2 |
Y | -2 | 0 | 2 |
GRAPH:
As we can see, both lines intersect at point (2,2) and hence the solution of both equations is x = 2 and y = 2.
Answer:
Given Equations,
Comparing these equations with
It is observed that;
It means the given equations have no solution, and thus the pair of linear equations is inconsistent.
Answer:
Let
Now, according to the question, the length is 4 m more than its width, so we can write it as
Or,
Also given Half Parameter of the rectangle = 36 it means
Now, as we have two equations, add both equations, and we get,
We get the value of
Now, putting this in equation (1), we get;
Hence, the Length and width of the rectangle are 20m and 16m, respectively.
Answer:
Given the equation,
We know that the condition for the intersection of lines for the equations in the form
So any line with this condition can be
Proof,
Hence,
Therefore, the pair of lines has a unique solution, thus forming intersecting lines.
Answer:
Given the equation,
As we know that the condition for the parallel lines for the equations in the form
So any line with this condition can be
Proof,
Hence,
Therefore, the pair of lines has no solutions; thus lines are parallel.
Answer:
Given the equation,
As we know that the condition for the coincidence of the lines for the equations in the form
So any line with this condition can be
Proof,
Hence,
Therefore, the pair of lines has infinitely many solutions; thus lines are coincident.
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:
From the graph, we can see that both lines intersect at the point (2,3), and therefore the vertices of the Triangle are ( -1,0), (2,3) and (4,0). The area of the triangle is shaded with a green colour.
Also Read-
1. Graphical Representation of Linear Equations: The process includes plotting linear equations on Cartesian graphs by using tables of values to draw their resulting straight lines.
2. Finding Solutions through Intersection Points: The intersection point between two lines indicates all solutions of the system while offering accurate insights into the equations.
3. Understanding Consistency of Systems: Knowing about System Consistency involves examining the graph to identify the number of solutions, along with determining whether the system follows a consistent or inconsistent or dependent pattern.
4. Types of Solutions: Unique solutions when lines intersect, No solutions when lines remain parallel and Infinite solutions occur with coinciding lines.
5. Verification of Solutions: The final verification involves testing whether graphically obtained solutions match both equations through substitution and transforming these results into calculations for accuracy verification.
Also see-
Students must check the NCERT solutions for class 10 of Mathematics and Science Subjects.
As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters
Students must check the NCERT Exemplar solutions for class 10 of Mathematics and Science Subjects.
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.
Admit Card Date:17 April,2025 - 17 May,2025
Exam Date:01 May,2025 - 08 May,2025
Result Date:05 May,2025 - 05 May,2025
Hello
Since you are a domicile of Karnataka and have studied under the Karnataka State Board for 11th and 12th , you are eligible for Karnataka State Quota for admission to various colleges in the state.
1. KCET (Karnataka Common Entrance Test): You must appear for the KCET exam, which is required for admission to undergraduate professional courses like engineering, medical, and other streams. Your exam score and rank will determine your eligibility for counseling.
2. Minority Income under 5 Lakh : If you are from a minority community and your family's income is below 5 lakh, you may be eligible for fee concessions or other benefits depending on the specific institution. Some colleges offer reservations or other advantages for students in this category.
3. Counseling and Seat Allocation:
After the KCET exam, you will need to participate in online counseling.
You need to select your preferred colleges and courses.
Seat allocation will be based on your rank , the availability of seats in your chosen colleges and your preferences.
4. Required Documents :
Domicile Certificate (proof that you are a resident of Karnataka).
Income Certificate (for minority category benefits).
Marksheets (11th and 12th from the Karnataka State Board).
KCET Admit Card and Scorecard.
This process will allow you to secure a seat based on your KCET performance and your category .
check link for more details
https://medicine.careers360.com/neet-college-predictor
Hope this helps you .
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.
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As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters
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