Question

Linear Equation in one variable

Define :-

■ Introduction
■Linear Equation
■ Rules for solving a Linear Equation
■ Solving Equations Having Variable on One side
■ Solving an equation having variable on both sides
■Applications of Linear Equation..

Answer 1

● Introduction :-

Any algebraic expression can be an equation when it contains an 'equal to' sign.

Algebraic Expesssion :
$2x {}^{2} + 3y + 9 \: and \: a {}^{2} + 3ab + b {}^{2}$

Equations: An equation is a statement of quality of two algebraic expressions which involves one or more variable.

Example :
$7x {}^{2} + 9xy + y {}^{2} = 20$

●Linear Equation :-

A Linear Equation is an equation involving only linear polynomials, i.e., where the highest power of the variable is one.

Example :
$3x + + 4 = - 3 \: \: and \: ax + by = c \: \\ and \: \frac{7}{3} x + \frac{4}{5} y = 2$
are linear Equations.

• Linear Equation in one variable : An equation of the first degree (i. e., linear) involving only one variable is called linear Equation in one variable.

Example :
$4x - 6 = 11 \: and \: 7x + 8 = 36$
are linear Equations in one variable.

● Rules for Solving a Linear Equation :

An equation remains the same, it doesn't change if :

1. Add the same number of both sides of the Equation.

2.Subtract the same number from both sides of the Equation.

3. Both sides are multiplied by the same non-zero number.

4. Both sides are divided by the same non-zero number.

By transposing any term of the equation to the other side by changing its sign from :

(a) + to -
(b) - to +
(c) × to ÷
(d) ÷ to ×

● Solving Equations Having Variable on One side :

An easy way of solving such questions is to bring the variable terms on one side and the numbers on the other side of the equality.

● Solving an equation having variable on both sides :

To solve an equation of this type we bring the variable terms on one side of the equality sign and constants, that is, numbers not solving variables, to the other side.

● Applications of Linear Equations :

We can make use of linear equations to solve many problems we encounter in our daily life. We have to first understand the problem and find out (a) What is given ? (b) What is required ? Then follow the steps as mentioned below :

Step 1. The required amount/quantity etc. are unknown. Let us represent the unknown value by English letters a,b,c,d,x,y,z.etc.

Step 2. Study the problem. Use logic and make a mathematical statement in the form of equation.

Step 3. Solve the equation to find out the value of unknown.

Step 4. Put the value in the equation and find out is LHS=RHS.


Thanks.

Answer 2

● Introduction :-

Any algebraic expression can be an equation when it contains an 'equal to' sign.

Algebraic Expesssion : 
2x {}^{2} + 3y + 9 \: and \: a {}^{2} + 3ab + b {}^{2}2x2+3y+9anda2+3ab+b2 

Equations: An equation is a statement of quality of two algebraic expressions which involves one or more variable.

Example : 
7x {}^{2} + 9xy + y {}^{2} = 207x2+9xy+y2=20 

●Linear Equation :-

A Linear Equation is an equation involving only linear polynomials, i.e., where the highest power of the variable is one.

Example : 
\begin{lgathered}3x + + 4 = - 3 \: \: and \: ax + by = c \: \\ and \: \frac{7}{3} x + \frac{4}{5} y = 2\end{lgathered}3x++4=−3andax+by=cand37​x+54​y=2​ 
are linear Equations.

• Linear Equation in one variable : An equation of the first degree (i. e., linear) involving only one variable is called linear Equation in one variable.

Example : 
4x - 6 = 11 \: and \: 7x + 8 = 36 \ 
are linear Equations in one variable.

● Rules for Solving a Linear Equation :

An equation remains the same, it doesn't change if :

1. Add the same number of both sides of the Equation.

2.Subtract the same number from both sides of the Equation.

3. Both sides are multiplied by the same non-zero number.

4. Both sides are divided by the same non-zero number.

By transposing any term of the equation to the other side by changing its sign from :

(a) + to -
(b) - to +
(c) × to ÷
(d) ÷ to ×

● Solving Equations Having Variable on One side :

An easy way of solving such questions is to bring the variable terms on one side and the numbers on the other side of the equality.

● Solving an equation having variable on both sides :

To solve an equation of this type we bring the variable terms on one side of the equality sign and constants, that is, numbers not solving variables, to the other side.

● Applications of Linear Equations :

We can make use of linear equations to solve many problems we encounter in our daily life. We have to first understand the problem and find out (a) What is given ? (b) What is required ? Then follow the steps as mentioned below :

Step 1. The required amount/quantity etc. are unknown. Let us represent the unknown value by English letters a,b,c,d,x,y,z.etc.

Step 2. Study the problem. Use logic and make a mathematical statement in the form of equation.

Step 3. Solve the equation to find out the value of unknown.

Step 4. Put the value in the equation and find out is LHS=RHS.


Thanks.