Multiply the first equation by 4, then multiply the second equation by 3. That will make the coefficients on y in the two equations additive inverses.
Next, add the two equations term by term to eliminate (hence the name of the method) the y variable, leaving you a single equation in x that can be solved by ordinary algebraic means.
Once you have determined the value of x, substitute that value into either of the original equations and then solve the resulting single-variable equation in y.
The x and y values determined above will give you the coordinates of the ordered pair that represents the single element of the solution set to the system of equations.
Note: In the event that the elimination process results in a trivial identity, i.e. 0 = 0, then you have a system of two equations that represent the same straight line in meaning that you have infinite solutions to the system. In the event that the elimination process results in an absurdity, such as 0 = 3, then you have the representation of two parallel lines and the solution set for the system is empty.
