What is an Elimination Method?

Elimination method is a method of solving a system of linear equations, which involves eliminating one variable from the system at a time, until only one variable is left. This method is often used to solve systems of equations that have three or more variables. The elimination method works by adding or subtracting equations to clear out one variable at a time.

Examples of Elimination Method

Let’s look at a simple example of an elimination method. Consider the following system of equations:

x + y = 4

2x + y = 6

In this example, we can use the elimination method to solve for x and y. First, we multiply the first equation by 2. This will eliminate the y variable, leaving only the x variable in the equation:

2(x + y = 4) → 2x + 2y = 8

Now, we subtract the second equation from the first equation:

2x + 2y = 8

2x + y = 6

–—————————

x = 2

Now, we can use the first equation to solve for y:

x + y = 4

2 + y = 4

–—————

y = 2

Therefore, the solution for this system of equations is x = 2 and y = 2.

Advantages and Disadvantages of Elimination Method

The elimination method is a useful tool for solving systems of equations that have three or more variables. It is also relatively straightforward and easy to understand. However, the method can become tedious when dealing with large systems of equations. Additionally, the method may not work if the equations are not compatible.