Example 1: Solve the system of equations by elimination Elimination Method Example Solution: In this example we will "cancel out" the y term. To do so, we can add the equations together. Elimination Method Solution Now we can find: x = 2 In order to solve for y, take the value for x and substitute it back into either one of the original equations. Elimination Method Solution The solution is (x, y) = (2, 1).