Maths CBSE Class 7 - Simple Equations

Simple Equations

Ø  An equation is a condition on a variable such that two expressions in the variable should have equal value. At least one of the expressions must contain a variable.

Ø  In an equation there is always an equal sign.

Ø  The value of the variable for which the equation is satisfied is called the solution (root) of the equation.

Ø  An equation remains the same if the LHS and RHS are interchanged.

Ø  Transposing means moving to the other side.

Ø  Transposition of a number has the same effect as adding same number to(or subtracting the same number from) both sides of the equation.

Ø  When we transpose a number from one side to other side of the equation, its sign is changed.

Ø  In case of the balanced equation, if we

(i)   Add the same number to both sides, or

(ii)   Subtract the same number from both the sides, or

(iii)   Multiply both sides by the same number, or

(iv)   Divide both sides by the same number, the balance remains undisturbed, ie the value of the LHS remains equal to the value of the RHS.

Examples of equation

2x+3=6,     y+1=7,   P - 3=10

Question

(1)   Write the following statements in equation form

(a)    The sum of numbers m and 16 is 60

Answer:  m+16=60

(b)   One fourth of  number y minus 7 is 12

Answer:  y/4 – 7=12

(2)   Write the following equation in statement form

(i)                 2m/3 =9

           Answer: Two-Third of m is 9

(ii)               n/2 + 5 = 10

    Answer: Add 5 to half of a number is 10

CBSE class IX -maths -chapter 4 - Linear Equations in Two Variable

Linear Equations in Two Variables

Definition

Any equation which can be put in the form ax+by+c=0, where a,b,c are real numbers and a,b are both not zero, is called a linear equation in two variables.

Ex. 2x+4y=18, 
   
      x+y=20

Note: The general form of a linear equation in two variable is ax+by+c=0

Exercise

1) The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement

solution:

 let the cost of a notebook to be Rs x and
cost of a pen to be Rs y.
The linear equation is 
               x=2y

or,       x-2y=0

2)Express the following equations in the form ax+by+c=0 and indicate the value of a,b and c

(i) -2x+3y=6

-2x+3y-6=0

a= -2, b=3, c= -6

(ii) 5=2x

2x-5=0
a=2, b=0, c= -5



Solution of a Linear Equation

Important points

• A linear equation in two variables has infinitely many solutions
• An easy way of getting a solution is to take x=0 and get the corresponding value of y. Then put y=0 and get the value of x.
• the solution of a linear equation is not affected when (i) the same number is added to (or subtracted from) both sides of the equation (ii) multiply or divide both the sides of the equation by the same non zero number.
• The solution of the linear equation in two variable is written as ordered pair (x,y)

Exercise

(1) Find the value of k, if x=2, y=1 is a solution of the equation 2x+3y=k

Answer

Given that x=2, y=1 is a solution of 2x+3y=k

Therefore 2*2  + 3*1= k

                           4+3 = k

                                7= k

                                k=7 

(2)  Find four solutions of 2x+y=7

    2x+y=7

Take x=0,
2*0 + y =7
0+y=7
y=7

(0,7) is a solution

Take y=0,
2x+0=7
2x=7
x=7/2

(7/2,0) is a solution

Take x=1,
2*1+y=7
2+y=7
y= 7-2
y=5

(1,5) is a solution

Take y=1,
2x+1=7
2x=7-1
2x=6
x=6/2
x=3
(3,1) is a solution


Home Work

1) Find the value of k, if x=1, y=5 is solution of  25x+10y=k

2) Is (3,0) is a solution of the equation 5x+2y=15.

Simultaneous Linear Equations

Consider  two linear equations in two variables x and y, 2x-y=3, 3x+2y=8
then we call these equations are simultaneous linear equations.

How to solve Simltaneous Linear Equation?

There are different methods to to find solution

1.Method of substitution

consider two equations   2x-y=3 and 3x+2y=8

2x-y=3..............(1)
3x+2y=8...........(2)

from equation (1),  y=2x-3...........(3)

substitute this in 2nd equation, 3x+2y=8

3x+2(2x-3) = 8

3x+4x-6 =8

7x=8+6

7x=14

x=14/7

x=2

From equation (3),  y=2x-3

y=2×2 - 3

y=4-3

y=1

x=2, y=1 is the solution

Question
Solve the equations x-y=2, x-3y=12

Mathematics Class 10. Part 1- Linear Equation Introduction

Chapter 1: LINEAR EQUATIONS IN TWO VARIABLE

• Defn: An equation which contains two variables and the degree of each term containing variable is one, is called a linear equation in two variable.

Ex: 2x+3y=10,  x+y=8

• General form of a linear equation in two variable is ax+by+c=0,

where a,b,c are real numbers and a, b are not equal to zero at the same time.
and x,y are variables

Ex. Consider the equation 7x-3=4y
 We can write the above equation as 7x-4y=3 (general form)

Examples of linear eqation in two variable

1)4m+3n=12
2)4/x + 5/y =16


Questions

1) Is √2 x - √5 y = 16, a linear equation in two variable?

2) what is the degree of a linear equation in two variable?


please answer this simple questions in comments.