Class 8 Exam  >  Class 8 Notes  >  NCERT Textbooks & Solutions for Class 8  >  Ex 2.1 NCERT Solutions: Linear Equations in One Variable

NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable


The linear equations in one variable is an equation which is expressed in the form of ax+b = 0 or ax+b= c, where  x is a variable, a is the coefficient of x, b and c are constants

  • For example, 2x+3=8 is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is x = 5/2. 

NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable

  • Whereas if we speak about linear equations in two variables, it has two solutions.

Let's have a look at NCERT Solutions of Linear Equations in One Variable:

Solve the following equations

Q1. x – 2 = 7 
Ans:  Transposing (–2) to RHS, we have:
⇒ x = 7 + 2
∴ x = 9

Note: By transposing a term from one side to another side, we mean changing its sign and carrying it to the other side. 

Q2. y + 3 = 10 
Ans: Transposing 3 to RHS, we have:
 y = 10 – 3
∴ y = 7


Q3. 6 = z + 2
Ans: Transposing 2 to LHS, we have:
⇒ 6 – 2 = z 
⇒ 4 = z
∴ z = 4


Q4. (3/7) + x = (17/7) 
Ans: Transposing 3/7 to RHS, we have:
NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable
= 14/7
= 2
 

Q5. 6x = 12
Ans: Dividing both sides by 6, we have:
NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable
∴ x = 2


Q6. (t/5) = 10 
Ans: Multiplying both sides by 5, we have:

NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable

∴ t = 50

Q7. (2x/3) = 18
Ans: Multiplying both sides by 3, we have:
NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable

⇒ 2x = 54

Dividing both sides by 2, we have:

NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable
x = 54/2 = 27

∴ x = 27 

Q8. 1.6 = (y/1.5) 
Ans: Multiplying both sides by 1.5, we have:

NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable
NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable
2.4 = y
∴ y = 2.4

Q9. 7x – 9 = 16

Ans: Transposing (–9) to RHS, we have:
7x = 16 + 9 = 25

Dividing both sides by 7, we have:

NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable

∴ x = 25/7

Q10. 14y – 8 = 13
Ans: Transposing –8 to RHS, we have:
14y = 13 + 8 = 21
Dividing both sides by 14, we have:

NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable
  NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable

∴ y = 3/2

Q11. 17 + 6p = 9
Ans: Transposing 17 to RHS, we have:
6p = 9 – 17 = –8
Dividing both sides by 6, we have:

NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable
 NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable

∴  NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable

Q12. (x/3) + 1 = (7/15)
Ans: Transposing 1 to RHS, we have:

NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable
 NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable

Multiplying both sides by 3, we have:
NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable

∴ x = - 8/5

The document NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable is a part of the Class 8 Course NCERT Textbooks & Solutions for Class 8.
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FAQs on NCERT Solutions for Class 8 Maths Chapter 2 - Ex 2.1 Linear Equations in One Variable

1. What are linear equations in one variable?
Ans. Linear equations in one variable are equations that involve only one variable and have a degree of 1. They can be represented in the form ax+b=0, where a and b are constants and x is the variable. These equations can be solved to find the value of the variable that satisfies the equation.
2. What are the methods to solve linear equations in one variable?
Ans. There are various methods to solve linear equations in one variable such as the method of substitution, method of elimination, and graphical method. The method of substitution involves substituting the value of one variable in the equation to find the value of the other variable. The method of elimination involves adding or subtracting equations to eliminate one variable and solve for the other variable. The graphical method involves plotting the equation on a graph and finding the point where the graph intersects the x-axis.
3. How are linear equations in one variable used in real-life situations?
Ans. Linear equations in one variable are used in various real-life situations like calculating profit and loss, determining the speed of a moving object, finding the cost of an item, and predicting the future value of an investment. These equations help in making predictions and decisions based on mathematical calculations.
4. What is the importance of learning linear equations in one variable?
Ans. Learning linear equations in one variable is important as it helps in understanding basic mathematical concepts and lays the foundation for more complex mathematical topics. It also helps in solving real-life problems and making informed decisions. Linear equations in one variable are also used in various fields like finance, engineering, and science.
5. What are the common mistakes to avoid while solving linear equations in one variable?
Ans. Some common mistakes to avoid while solving linear equations in one variable include forgetting to distribute negative signs, making calculation errors, not checking the solution, and not simplifying the equation. It is important to double-check the solution to ensure that it satisfies the equation and to simplify the equation as much as possible to avoid confusion.
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