How do you do the elimination method in systems of equations?

You balance one of the unknowns in the equation then divide the coefficient of the unknown by itself

You need to have either the coefficients of the x values or the coefficients of the y values be opposites. When you add the two equations the opposites will cancel the x or y leaving only one variable to work with. After solving for that variable, plug it into either of the original equations to solve for the remaining variable.