Linear Equations Class-8 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Chapter-15. We provide step by step Solutions of Exercise / lesson-15 Linear Equations for ICSE Class-8  RS  Aggarwal Mathematics.

Our Solutions contain all type Questions of Exe-15 A, Exe-15 B, Exe-15 C (MCQ) with Notes to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-8 Mathematics.

## Linear Equations Class-8 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Chapter-15

-: Select Topic :-

Notes on Linear Equations

EXE-15 A,

EXE-15 B,

MCQ EXE-10 C,

### Notes on Linear Equations

Linear Equations Class 8 Notes- Chapter 15- The solution to this linear equation can be any rational number. This equation may consist expressions which are linear on both sides of the equal to sign. Just like numbers, we can also transpose the variables from one side of the equation to the other side.

#### Equation:

An equation is a statement of equality which contains one or more unknown quantity/ quantities (or variable/variables) is called an equation.

#### Solving an Equation:

Solving an equation means determining its root i.e., determining (finding) the value of the variable which satisfies it.

1.  Rules for solving a linear equation in one variable:-
Add the same number on both the sides of the equation.
Subtract the same number from both the sides the equation.
Multiply both the sides of the equation by the same number.
Divide both the sides of the equation by the same non zero number.
Transpose a term from LHS to RHS or vice-versa.
2.  Transposing means taking a term from one side to the other side of an equation while changing its sign.
3.  The highest power of a linear equation is always one.
4.  An equation may have linear expressions on both sides of the equation.
5.  Such equations help us to solve various problems based on numbers, age, perimeters, combination of coins etc

### Stepwise procedure to solve a word problem.

• Read the given word problem carefully and identify what is given and what is required.
• Use letters x, y, z, etc. to represent the unknown quantity.
• Transform the statements of the problem into mathematical statements.
• Form the linear equation according to the given condition (s) of the problem.
• Solve the equation by the usual method.
• Check the solution for its validity.
• Reject if the solution is invalid

### Solving Equations having the Variable on Both Sides

We transpose the terms in such a manner that the terms containing the variables are on the LHS and constant numbers on RHS.
Then, simplifying both sides and dividing by a suitable number (if required), we can solve the equation.
Finally, check the validity of the solution obtained. Reject if the solution is invalid

### Reducing Equations to Simpler Form

We multiply both sides of the equation by the LCM of the denominators of the terms in the expressions occurring in the given equation.

We transpose properly so that all the variable terms come on LHS and constant terms on RHS.
Then, combining like terms on both sides of the equation and dividing both sides by a suitable number (if required), we can find out the required solution.
Finally, we check this solution for its validity. Reject if the solution is invalid

#### Equations Reducible to Linear Form

Sometimes the given equation is not linear in form. By cross-multiplication and further simplification, it can be transformed into a linear equation in one variable. Then, it can be solved by the usual method.

Exe-15 (A )

### Linear Equations Class-8 RS Aggarwal ICSE Maths Goyal Brothers Prakashan

Solve the following equation

Question 1

4 x – 9 = 2 x + 7

Question 2

5 y + 18 = 11 – 2y

Question 3

21 – 3(x-7) = x + 20

Question 4

3 (y-7) – 2 ……………

Question 5

3 (t-5) – 16 t = 12 -2 (t-3)

Question  6

……………….

……………………..

…………………….

Question 15

(z+3) (z-3) – z (z+5) = 6

Question 16

y (2y + 3) – 2y(y – 5) = 26

Question 17

…………………..

Question 18

3/4 ……………………..

### Exe-15 (B),

Linear Equations Class-8 RS Aggarwal ICSE Maths Goyal Brothers Prakashan

Question 1

17 is less than four time a number is11. Find the number.

Question 2

If 10 be added ………………. Find the number.

Question 3

…………………………

………………………

………………………

Question 9

A number when …………………. Find the number.

Question 10

Four-fifths of a number ……………………… find the number.

Question 11

…………………….

…………………..

……………………

Question 19

The sum of …………………….. find the original number.

Question 20

What same number ………………… are in proportion ?

Question 21

……………………….

………………………

………………………

Question 29

A man is five …………………….. present ages.

Question 30

A man is twice ……………….. present ages.

Question 31

………………………

………………………

…………………….

Question 38

A boat …………………….. in still water.

Question 39

The length of each ……………………….. sides of the triangle.

Question 40

………………………..

………………………..

…………………………

Question 44

Divide 600 in two parts such that 40 % of one exceeds 60 % of the other by 120.

Question 45

A workman is paid …………………….. For how days did he remain abest ?

MCQ Exe-15 (C),

### Linear Equations Class-8 RS Aggarwal ICSE Maths Goyal Brothers Prakashan

Choose the correct option in each of the following

Question 1

If …………………………

Question  2

…………………….

………………………

……………………

Question 11

the age of a ………………… daughter is

Question 12

……………………

…………………….

…………………..

Question 19

For aiming at …………………. the target.

Question 20

A total of ………………… coins is.

–: End of Linear Equations Class-8 RS Aggarwal  Solutions :–

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