Skip to content 
How to create and solve Linear and quadratic equations
Before you study the NCERT textbook of tenth class maths, the linear equations, and quadratic equations, you have to understand how to create and solve algebraic equations from a given algebraic question. The linear equations and quadratic equations both are in the curriculum of X class of every board weather it is CBSE, ICSE or any other state board of the world. In CBSE board almost 25 marks of the total 80 marks questions are asked in the final board exam of X class from the chapters of linear equations in two variables and quadratic equations. Future Study Point is introducing here few tips of solving quadratic and pair of linear equations through the solution of a few examples, once you go through the whole of the post you might become an expert in both of the lessons and you would be capable to grab hundred percent marks in the questions asked from the lessons of linear equations and quadratic equations.
How to create and solve Linear and quadratic equations
NCERT Solutions Class 10 Science from chapter 1 to 16
After you go through this post on linear and quadratic equations you will become confident and you could solve all the unsolved questions of linear and quadratic equations of your textbook like NCERT or of other guides like R.D Sharma. Here each question of linear and quadratic equations is literally explained step by step in such a way that you could clear all your doubts in building a pair of linear equations or quadratic equations.
You can also study
Number System (all types of numbers used in maths)
What are Surds and how to compare them ?
Three ways of solving quadratic equations
Achieve hundred percentage marks in maths
The difference between rational and irrational numbers
Solutions of the questions based on expression and equations
Tips of developing memory power and qualifying a government entrance exams
Tips to get success in competitive exams
Lines, angles and triangles for 6 th to 10 th class cbse geometry
Finding the roots of the polynomial by the complete square method
Three Ways of Solving Quadratic Equations
Addition, subtraction, multiplication and division of polynomials
Please follow us on pintrest
NCERT Solutions Class 10 Science from chapter 1 to 16
NCERT Solutions of all chapters of Maths for Class 10 from Chapters 1 to 15
NCERT Solutions of Class 9 Science : Chapter 1 to Chapter 15
NCERT Solutions of Class 9 Maths : from chapter 1 to 15
Class 10 Biology Viva Voce Questions and Answers for CBSE Board 2020-21
Class 10 Physics Viva Voce Questions for CBSE Board 2020-21
Class 10 chemistry Viva Voce Questions and Answers for CBSE Board 2020-21
Class 10 Chemistry Practical Based Questions for CBSE 2020-21 Board Exam
Type of Chemical Reactions with Complete detail
Class 10 maths NCERT solutions of chapter 7- Coordinate Geometry
Class 10 Maths NCERT solutions of Chapter 6- Triangles
Ozone Layer and How it is Getting depleted.
Solutions of Class 10 maths question paper Set-3 CBSE Board 2019
CBSE Class 10 science question paper 2020 SET -3 solutions
Science and Maths NCERT solutions for Class 9 ,10 and 11 classes
How to create and solve Linear and quadratic equations
Pair of linear equation in two variables→ In these questions you are given two statements in the questions in which two variables are related to each other. From these statements, you have to build up equation 1 and equation 2, thereafter you can evaluate both of the variables presented in the pair of linear equations. Here the solution of the linear equations is shown algebraically and not by the way of the graph because our main focus is to let you understand how to build a pair of the equations. Study the following examples.
Most popular mobile phones in Amazon: click here
How to create and solve Linear equations
Q1. Sita tells his daughter that 7 years ago she was 7 times as old as she were and after 3 years then she should be one-third of her age. Find the present ages of both.
Ans. In this question the first statement is 7 years ago Sita was 7 times as old as her daughter.
Here the age of Sita is given in terms of her daughter, so it is convenient to write the age of Sita(x) in the left part of the equation and in the right part write the age of her daughter(y)
x → y
7 years back, their ages
x – 7 and y – 7
7 years back Sita’s age = 7 × 7 years back her daughter’s age
x – 7 = 7( y- 7)
Simplifying it
x – 7 = 7y – 49
x – 7y = –42……….(1)
The second statement of the question is after 3 years Sita’s daughter becomes one-third of Sita’s age or Sita becomes thrice of her daughter’s age (because it is simple to write).
x → y
After 3 years their ages are
x + 3 and y + 3
Sita’s age after 3 years= 3 × Her daughter’s age after 3 years
x + 3 = 3(y + 3)
x + 3 = 3y + 9
x – 3y = 6………….(2)
x – 7y = –42……….(1)
Subtracting one eq.(1) from eq.(2)
We get y = 12, putting the value of y in equation (2), we get x = 42
Hence the age of Sita is 42 years and the age of her daughter is 12 years
Ex2. 5 men and 2 women do a piece of work in 4 days and 6 men and 3 women can do that work in 3 days . How many days a man or a woman alone can do the same work.
Ans. First of all, suppose the variables, you are asked in the question, here we have to suppose two-variable the number of days a man alone take to complete the work (x) and number of days a woman alone take to complete the work(y).
First statement of the question is 5 men and 2 women do a piece of work in 4 days
5× 1 day work of a man + 2 × 1 day work of a woman = 1 day work of 5 men and 2 women
Let’s find the one day work of man and of woman and 1 day work of 5 men and 2 women as follows.
In x day a man alone will do → 1 piece of work
In 1 day a man will do → (1/x) part of the work
In y days a woman alone do → 1 piece of work
In 1 day a woman alone will do→ (1/y) part of the work
According to first condition,5 men and 2 women do in 4 days → 1 piece of work
5 men and 2 women will do in 1 day →(1/4) Part of the work
Therefore the linear equation according to first statement is as follows
1 day work of 5 men = 5 × 1 day work of a man = 5× 1/x = 5/x
1 day work of 2 women = 2× 1 day work of a woman = 2× 1/y = 2/y
Therefore,we have
5/x + 2/y = 1/4……..(1)
Following the same procedure in building equation (2) from the second statement of the question.
6/x + 3/y = 1/3……..(2)
Multiplying (1) by 6 and eq.(2) by 5 ,we get the following equations (3) and (4)
30/x + 12/y = 3/2 ……(3)
30/x + 15/y = 5/3
Subtracting (4) from (3) we have
–3/y = –1/6
y = 18, putting this value in equation (1)
5/x + 2/18 = 1/4
5/x = 1/4 – 2/18
5/x = (9 –4)/36
x = 36
Therefore a woman alone can do that piece of work in 18 days and a man alone can do that work in 36 days.
How to create and solve the quadratic equation
Quadratic Equations. The equation in the form of ax² + bx + c =0 is known as a quadratic equation, there are certain questions which can be solved by the formation of either the system of linear or quadratic equations, few of the examples are given below.
Quadratic equations can be solved by the factorization method, complete squire method or by the quadratic formula.
Read our post the solution of quadratic equation by the complete squire method
Finding the roots of the polynomial by the complete square method
⇒Generally when product of two variable is given or manipulation of both statements become possible to form a single quadratic equation, then it is convenient for the students to solve it by the rule of the quadratic equation. See the examples.
Ex3. The product of two consecutive natural number is 420,find the numbers.
Ans. Let first number is x and second will be x +1
According to question x(x +1) = 420
x² + x –420 = 0
x² + 21x –20x –420 =0
x(x+ 21) –20(x + 21) = 0
(x+ 21)(x –20) = 0
x = 20,–21
Avoiding the number in negative sign because here number means the natural number
Therefore the natural numbers are x =20, x +1=21
Click for online shopping
Future Study Point.Deal: Cloths, Laptops, Computers, Mobiles, Shoes etc
NCERT Solutions of Science and Maths for Class 9,10,11 and 12
NCERT Solutions for class 9 maths
NCERT Solutions for class 9 science
NCERT Solutions for class 10 maths
CBSE Class 10-Question paper of maths 2021 with solutions
CBSE Class 10-Half yearly question paper of maths 2020 with solutions
CBSE Class 10 -Question paper of maths 2020 with solutions
CBSE Class 10-Question paper of maths 2019 with solutions
NCERT Solutions for Class 10 Science
NCERT Solutions for class 11 maths
| Chapter 1-Sets | Chapter 9-Sequences and Series |
| Chapter 2- Relations and functions | Chapter 10- Straight Lines |
| Chapter 3- Trigonometry | Chapter 11-Conic Sections |
| Chapter 4-Principle of mathematical induction | Chapter 12-Introduction to three Dimensional Geometry |
| Chapter 5-Complex numbers | Chapter 13- Limits and Derivatives |
| Chapter 6- Linear Inequalities | Chapter 14-Mathematical Reasoning |
| Chapter 7- Permutations and Combinations | Chapter 15- Statistics |
| Chapter 8- Binomial Theorem | Chapter 16- Probability |
CBSE Class 11-Question paper of maths 2015
CBSE Class 11 – Second unit test of maths 2021 with solutions
NCERT Solutions for Class 11 Physics
chapter 3-Motion in a Straight Line
NCERT Solutions for Class 11 Chemistry
Chapter 1-Some basic concepts of chemistry
NCERT Solutions for Class 11 Biology
NCERT solutions for class 12 maths
| Chapter 1-Relations and Functions | Chapter 9-Differential Equations |
| Chapter 2-Inverse Trigonometric Functions | Chapter 10-Vector Algebra |
| Chapter 3-Matrices | Chapter 11 – Three Dimensional Geometry |
| Chapter 4-Determinants | Chapter 12-Linear Programming |
| Chapter 5- Continuity and Differentiability | Chapter 13-Probability |
| Chapter 6- Application of Derivation | CBSE Class 12- Question paper of maths 2021 with solutions |
| Chapter 7- Integrals | |
| Chapter 8-Application of Integrals |
Class 12 Solutions of Maths Latest Sample Paper Published by CBSE for 2021-22 Term 2
Class 12 Maths Important Questions-Application of Integrals
Solutions of Class 12 Maths Question Paper of Preboard -2 Exam Term-2 CBSE Board 2021-22
Solutions of class 12 maths question paper 2021 preboard exam CBSE Solution
