To solve a system of equations with the addition method, follow these steps:

1. Rewrite both equations in standard form if they aren’t in it already.

2. Multiply the terms of the equations by some constant that will cause the first variable to have the same coefficient in both equations, but with opposite signs, i.e., ${\displaystyle 2y=3x+2}$ and ${\displaystyle -2y=4x-3}$ (both have ${\displaystyle 2y}$, but one of them has the opposite sign).

3. Add the equations together. The first variable will cancel out, leaving you with the second variable.

4. Solve the new equation for this variable.

5. Substitute the value you got in step 4 back into either one of the original equations, and solve for the remaining variable.

6. Plug both values back into the original equations and check the solutions.