Question

What is subsituting methord of linear equation?​

Answer 1

The solution of the simultaneous linear equation can be divided into two broad categories, Graphical Method, and Algebraic method. The substitution method is one of the categories of the algebraic method. In this article, let us discuss what is the substitution method, and how to solve the linear equation using the substitution method with examples.

Table of Contents:

Definition

Algebraic Method

Graphical Method

Steps

Elimination by Substitution Method

Difference Between Substitution and Elimination Method

Examples

FAQs

Substitution Method Definition

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation. In this way, a pair of the linear equation gets transformed into one linear equation with only one variable, which can then easily be solved. Before moving to solve the linear equations using the substitution method, we will discuss what is the algebraic method and graphical method.

Algebraic Method

An Algebraic method is a collection of several methods, which are used to solve a pair of the linear equation that includes two variables. Generally, the algebraic method can be sub-divided into three categories:

Substitution method

Elimination method

Cross-multiplication method

Graphical Method

The graphical method is also known as the geometric Method used to solve the system of the linear equation. In this method, the equations are designed based on the objective function and constraints. To solve the system of linear equations, this method has undergone different steps to obtain the solutions.

In this article, we will focus mainly on solving the linear equations using the first algebraic method called “Substitution Method” in detail.

Substitution Method Steps

For instance, the system of two equations with two unknown values, the solution can be obtained by using the below steps. Here, the list of steps is provided to solve the linear equation. They are

Simplify the given equation by expanding the parenthesis

Solve one of the equations for either x or y

substitute the step 1 solution in the other equation

Now solve the new equation obtained using elementary arithmetic operations

Finally, solve the equation to find the value of the second variable

Graphing of Linear Equations

Solving Linear Equations

Linear Equations in Two Variables

Difference Between Linear and Non-Linear Equations

Elimination by Substitution Method

In this method, the elimination of the variable can be performed by substituting the value of other variables in an equation. Hence, this method is called the elimination by substitution method.

Let us assume the system of linear equations

2x+3y = 13 and x-2y = -4

Given:

2x+3y = 13 … (1)

x-2y = -4 …(2)

The equation (2) can be written as

x = 2y-4 … (3)

Now, in equation (1) eliminate the variable x by substituting the equation (3)

Hence, equation (1) becomes

2(2y-4) +3y = 13

Now, apply the distributive property for the above equation,

4y-8+3y = 13

Now, solve the above equation for the variable y

7y – 8 = 13

7y = 13+8

7y = 21

y= 21/7

y= 3

Hence, the value of y is 3.

Now, substituting y=3 in the equation (2), we get

x- 2(3) = -4

x – 6=-4

x = -4+6

x = 2

Therefore, the value of x is 2.

Hence, the solution for the system of linear equations are:

x = 2 and y=3

To check whether the obtained solution is correct or not, substitute the values of x and y in any of the given equations.

Verification:

Use Equation (2) to verify the solution

x-2y = -4

Now, substitute x= 2 and y=3

2-2(3) = -4

2-6= -4

-4=-4

Here, L.H.S = R.H.S

Hnece, the obtained solution is correct.

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Answer 2

$\red{\bold{\underline{\underline{QUESTION:-}}}}$

:- what is substitution method of linear equation?

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:-Substitution method is a method in which we substitute the value of one variable and put into another equation to find out the value of another variable.

example :-x+y=10

x=10-y

let's suppose there is an another equation x+2y=8

now here we substitute the value of x to find out the value of Y

(10-y)+2y=8

10+y=8

y=-2

Hope it helps you..!!!!

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