How to Write a Linear Equation in One Variable and Two-Variable?

Linear equation in one or two variable are the questions which are part of the mathematics of all classes from class VI to XII, Linear equations in one variable and two variables are generally asked in competitive entrance exams here we are trying to resolve the problems of the student they face in building the equations. In the CBSE syllabus the linear equations in one variable start from class VI. Class VII has more complicated equations compared with VI and in-class VIII  it becomes tougher to build the linear equation. Further in class IX syllabus comprised of single linear equation in two variables and class X syllabus consist of two linear equations in two variables.

Future Study Point brings a way of easing the path of students by the explanation of building linear equations through a step by step method, here we will start from class VI. You have to point out the following precautions in building the equations.

(i) Read the statements in the questions carefully.

(ii) Pay attention what are the quantities compared.

(iii) The quantities are  compared to which one

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How to Write a Linear Equation in One Variable and Two-Variable?

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Example 1. The age of Shyam is two years more than Ram if the sum of both ages is 22 years, then find the age of both.

Solution. In the above question, the hint of ages of Ram and Shyam are given in which the age of Shyam is given in terms of Ram, so it will be convenient for you to suppose the age of Ram as following.

Let the age of Ram is x then the age of Shyam will become x + 2.

The sum of both ages is x + (x + 2)

According to questions, the sum of both ages is 22 years

Therefore as per the statements of questions

x + (x + 2) = 22

2x + 2 = 22

2x = 22 – 2

2x = 20

x = 20/2 = 10

The age of Ram (x) = 10 years and the age of Shyam = x +2 =10 + 2 = 12 years

Example 2. 20 is added to a number results 25.

Solution.

Let the number is x

20 is added to x it will become x + 20

The result is after the addition of 20 it becomes 25

According to question

x + 20 = 25

x = 25 –20 = 5

So, the required number is 5

Examples of linear equations of class VII.

The way of building equations is the same in every class, what makes the difference that is details or description of the questions.

Ex3- The age of Shyam is 2 years more than twice of Ram’s age, if the sum of both ages is 32 then find the ages of both.

Ans.

As compared to question(1) one more detail is given in this question i.e twice of Ram’s age in addition to two year more

Here in this question the age of Shyam is given in terms of Ram

Let the tha age of Ram is = x

The age of Syam is 2 year more than 2 × the age of Ram (x)

The age of Shyam = 2x + 2

According to question that sum of both ages x and 2x + 2 is 22

Therefore equation will become

x + 2x + 2 = 32

3x = 32 – 2 = 30

x = 30/3 = 10

Therefore the age of Ram is(x) =10 years and of Shyam will be 2×10 +2 =22 years

Example 4- If in a fraction 2 is added to the numerator and 3 is subtracted from its denominator then the fraction becomes  7/9. If the denominator is 2 more than twice of the numerator then find the fraction?

Ans- Here numerator and denominator are compared such that the denominator is 2 more than 2 × the value of the numerator

The value of the denominator is given in terms of the numerator, so letting its numerator = x

Its denominator will become = 2× x + 2 = 2x + 2

According to the question the fraction  = x/(2x +2)

According to second condition,we are given that after  2 is is added to numerator and 3 is subtracted from denominator fraction becomes  7/9

Therefore according to the questions, the following equation is build-up

9x  + 18 = 14x + 14 – 21

9x – 14x = 14 – 21 – 18

–5x = 14 – 39

–5x = –25

x = –25/–5 = 5

Therefore the numurator = 5

Denominator = 2 × 5+ 2 = 10+2 =12

The fraction will be = (Numerator/Denominator)= 5/12

Therefore the fraction is = 5/12

Science and Maths NCERT solution for Class 9 to 11 class

Example 5. years back the age of sonu was twice the age of his sister and the sum of their ages was 45.

Ans. We are given here the  5 years back age of Sonu in terms of 5 years back age of his sister

Therefore the age of his sister = x

5 years back she would be of the age = x –5

5 years back the age of Sonu = 2(x –5)

2(x –5) + x –5 = 15

2x – 10 + x –5 = 15

3x  = 60

x = 20

Example6-5 years back the age of Sonu was 2(x –5) = 2(20 –5) = 30, therefore his present age will be 30 +5= 35 years.

Ex 6- Sum of a two-digit number is 3 if 9 is added to it , it is reversed.

Ans. Let tense of two-digit number = x and ones of the number = 3 – x

The way of writing a two-digit number is as follows

Therefore the number will be = 10x + 3 –x =9x + 3

When digits of number reversed tense is 3 –x and  ones is x

The number will become = 10(3 – x) + x = 30 – 10x + x = 30 –9x

According to question

9x + 3 + 9 = 30 –9x

18x = 18

x =1

Therefore one of the digit or tense is 1 and another digit or ones is 3 – 1 = 2

The number will be = 12

Linear equation in two variables is the maths lesson in class 9 

How to Write a Linear Equation in One Variable and Two-Variable?

Example 7.As an example Sita is 2 years more than his brother’s age,write it in the form of an equation.

Ans. The age of Sita and the age of her brother are related to each other in which age of Sita is given in terms of his brother’s age, here two-variable are Sita’s age and her brother’s age.

Let Sita’s age is = x and her brother’s age = y

 x   = y + 2

In this equation for every value of y there are infinite solutions of x

The solution of such an equation is always shown by the graph.

Linear equation in two variable- If two lines are intersecting in the graph then both have a single unique solution and if they are parallel then the pair of equations doesn’t have any solution and if pair of the equation are representing the same line then the pair of the equations have the infinite solution.

The algebraical solution of a pair of linear equation-Ex 8. Sum of a two-digit number is 3 if 9 is added to it , it is reversed.

Ans. Let the tense digit of two-digit number  = x and one’s digit is y

According to first condition x + y = 3……….(i)

The number = 10x + y   and after reversing it become = 10y + x

According to the second condition

10x + y  + 9 = 10y + x 

9x – 9y = –9 ⇒x –y = –1…………….(ii)

Adding both equations we get x = 1 and then putting it in (i) we have y= 2

Therefore the required number is 12

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