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The correct method to find the solution to a system of equations is substitution or elimination.

Using substitution involves solving one equation for one variable and then substituting that expression into the second equation, allowing for a straightforward solution of the variables. This method is particularly useful when one equation is easily manipulated to isolate a variable.

Alternatively, elimination focuses on adding or subtracting equations to eliminate one variable, making it possible to solve for the other. This is effective when the equations can be easily aligned in terms of coefficients for one variable.

Both methods are standard approaches in algebra that are widely taught and applicable to most systems of linear equations, making this choice the most reliable for systematically finding solutions to such equations.

The other methods listed, while they may have specific applications in mathematics, are not standard techniques for solving systems of equations. Factorization primarily applies to polynomials, and the resultant method is generally used in polynomials to find values common to two equations rather than direct solutions. The addition of coefficients is not a recognized method for solving systems and would not yield a solution.