When solving systems of linear equations using the elimination method, there are some simple steps to follow. Here’s how I usually do it:

1. Write the equations: Start by writing down the two equations you need to solve. For example:

   $$2x + 3y = 6$$ $$4x - y = 5$$

2. Align the equations: Make sure both equations are in standard form, which means all the terms are on one side of the equals sign.

3. Manipulate the equations: To eliminate one variable, you might need to multiply one or both equations by a number. For example, if you want to eliminate ( y ), you could multiply the second equation by 3.

4. Add or subtract the equations: Now, combine the two equations. The goal is to eliminate one variable. It would look something like this:

   $$2x + 3y + (12x - 3y) = 18 + 5$$

5. Solve for the remaining variable: Once you’ve removed one variable, you can solve for the other variable.

6. Back substitute: Finally, take the solution you found and plug it back into one of the original equations to find the other variable.

And just like that, you've solved the system!