The elimination method, also known as the addition/subtraction method, is a powerful technique used to solve systems of linear equations. This method involves eliminating one variable by adding or subtracting the equations in a strategic way.

To solve a system of linear equations using the elimination method, follow these steps:

1. Write the equations in standard form
2. Determine which variable to eliminate
3. Multiply one or both equations by suitable constants so that when added or subtracted, one of the variables will cancel out
4. Add or subtract the equations to eliminate the chosen variable
5. Solve the resulting equation for the remaining variable
6. Substitute the value obtained back into one of the original equations to find the value of the eliminated variable

Let's illustrate this method with an example:

Example: Solve the system of equations

2x + 3y = 7
4x + 5y = 14

Step 1: Write the equations in standard form:

2x + 3y = 7
4x + 5y = 14

Step 2: Determine which variable to eliminate. In this case, let's eliminate the variable x.

Step 3: Multiply the first equation by -2 and the second equation by 1 so that when added, the x terms will cancel out.

-4x - 6y = -14
 4x + 5y = 14

Step 4: Add the equations to eliminate x.

-1y = 0
 y = 0

Step 5: Substitute the value of y back into one of the original equations.

2x + 3(0) = 7
 2x = 7
 x = 7/2

So, the solution to the system of equations is x = 7/2 and y = 0.

By using the elimination method, we can efficiently solve systems of linear equations and find the values of the variables.