When you're working with linear equations, there are some common mistakes you want to avoid. Here are a few tips to help you out:

1. Get the Standard Form Right: It's important to write the equation in standard form, which looks like this: $Ax + By = C$.

   For example, $2x + 3y = 6$ is in standard form, but $3y = 6 - 2x$ is not.

2. Watch the Coefficients: Be careful with the signs in front of the numbers (called coefficients).

   For instance, $-x + 4y = 8$ and $x - 4y = -8$ show different lines.

3. Don't Forget to Simplify: Always try to simplify your equations if you can.

   For example, instead of writing $4x + 8y = 12$, you can simplify it to $x + 2y = 3$.

4. Understand What the Solutions Mean: Remember that the solution to a linear equation represents a whole line, not just one point.

By avoiding these mistakes, you'll get better at handling linear equations!