The strategy for solving by elimination is to find a multiplier for one or both of the equations such that you make the coefficient on one of the variables in one of the equations be the additive inverse of the coefficient on that same variable in the other equation.
In the case of given example, you don't have to find a multiplier for either equation because you already have a coefficient of 1 on x in the first equation and a coefficient of -1 on x in the second equation.
Just add the two equations, term-by-term. Since you will be adding x to -x, you will end up with 0x, effectively eliminating (hence the name of the method) that variable. The end result will be a single equation in one variable, in this case, y. Solve for the remaining variable, and then use this value to substitute back into either of the original equations in order to solve for the variable that you eliminated.
