Elimination Method: Explained with Calculations

The elimination method is used to explain a linear equation and it is the most common term used for resolving the system of linear equations. In this method, we exclude any one variable with the help of an elementary (primary) arithmetic operation then we make the simple equation for the search for another variable.

With the help of identifying variables, we know the value of an excluded variable. For easy calculation, we mostly use the elimination method because with the help of it we wave-off a variable and find the value of the other variable.

Further in this article, we’ll learn the basic definition of the “Elimination method” its structure, and how it works.

Definition of Elimination Method

The term “elimination” means to eliminate something. The Elimination Method, also known as the Addition/Subtraction Method, is a technique used to solve a system of linear equations involving two or more variables.

In this method, the goal is to eliminate one of the variables by adding or subtracting the equations in the system to create a new equation with only one variable. Once one variable is eliminated, the system is reduced to a simpler form, making it easier to find the values of the remaining variables.

Also read: IGCSE Math Extended Exhaustive Syllabus

Structure of resolving equation by Elimination method:

In the elimination method, first of all, we check the constant of the variable in the equations if the same with the opposite sign, then add both equations and exclude the one variable. And find the value of the remaining variable and put it in any given equation and get the value of an excluded variable. See the example.

Example 1:

The Given equations are.

2X – Y = 5                      (1)

X + 2Y = 7                      (2)

Solution                                 

Step 1: Make a like variable

Multiply equation (2) by “2”

2 * (X + 2Y) = 2 * (7) by multiplying we get

2X + 4Y = 14                 (3)

Step 2: Subtraction

Now subtract equations (1) and (3)

2X – Y = 5

-(2X + 4Y) = -14 by subtracting equations

-5Y = -9

Y = 9 / 5

Step 3:

Now put the value of the known variable in any given equation and find the value of the excluded variable.

Put the value of “Y” in any given equation. We decide to put in (1)

2X – (9 / 5) = 5

10X – 9 = 25 (by lcm)

X = (25 + 9) / 10

X = 34 / 10

X = 17 / 5

Step 4:

For checking whether our values are correct or not so put the values of X and Y in any equation if both sides are equal then our values are correct.

2(17/5) – (9/5) = 5

25=25 so our finding values are correct.

Solving steps for elimination Method

• Fix which variable is excluded. If essential then alter both equations and make the constant of each variable the additive inverse.
• With the help of adding combine both equations and make sure only one variable remains.
• Explain the equation for the residual variable
• Put the value of the remaining variable in the unique equation and find the value of the excluded variable.
• Plug the values into any equation to satisfy your answer. If the response is the same on mutual sides, then your values are correct.

The steps which are used to solve the linear equations.

Examples

Let’s some examples do for the clearance of the elimination method.

Example 1

Consider two linear equations

X + Y = 8                                  (1)

3X – 2Y = 9                               (2)

Solution:

Step 1:

According to the above steps first, we fix excluded variable now we exclude Y for this multiply equation (1) with” 2”

2(X + Y) =2 (8)

2X + 2Y = 16                            (3)

Step 2:

Now we add both equations (3) and (2)

2X + 2Y = 16

3X – 2Y = 9       (By adding equations)

5X = 25

X = 5

Step 3:

By putting the value of X in the original equation (1) we got the value of the excluded variable

5 + Y = 8

Y = 3

Step 4:

Now put the values of X and Y in any equation

5 + 3 = 8

8 = 8

Therefore, our finding values satisfied the equation

The problems of solving system of linear equation by elimination method can also be evaluated with the help of an elimination calculator to get rid of time-consuming calculations.

Elimination method: Nope solution

Every parallel line equation has no solution. if we solved any type of parallel line equation by using the elimination method, we get no solution because, in this type of equation, we cannot eliminate one variable both variables are eliminated. For sample

4X – 2Y =10                  (1)

2X – Y = 9                    (2)

If we try to eliminate one variable and multiply equation (2) with “2” then both variables are eliminated and

We have no solution. So, the equations are similar.

Elimination method: Extreme solutions

Coincident line equations have many possible solutions. So, if try to solve the coincident line equation with the elimination method we get reliable with many solutions. In this type of case, we get a solution in 0 = 0 form,

By spreading the elimination method. For example, we take the equations

X + Y = 3

3X + 3Y – 6 =0

So, if we multiply any non-zero constant number with any equation for excluding variable, we see both variables are eliminated and we got the solution in 0=0 form this means these equations have many solutions.

It is the one of methods to know how many solutions to these equations before applying the elimination method.

Also Read: Beyond the Trillions: Discovering the Unfathomable Names of Larger Numbers

Conclusion

In this article, we discussed the introduction, and definition and tried to cover the concept of this topic with the help of examples. We have discussed the steps which are used to solve elimination problems. Structure of resolving elimination method.