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A system of equations is a set of more than one equation, each sharing a common variable. In the given exercise, we are dealing with a system of two equations where both equations involve the variables 'x' and 'y'. The objective is to find the values of these variables that satisfy both equations simultaneously.

When solving systems of equations, there are multiple methods to choose from, such as graphing, substitution, elimination, and matrix operations. The choice of method typically depends on the form and complexity of the system. In the exercise, we use the substitution method, which is highly effective when one of the equations can easily be solved for one of the variables, as it is the case with the first equation, where solving for 'x' is straightforward.

Factoring quadratics is a key concept in algebra. A quadratic equation typically has the standard form \( ax^2 + bx + c = 0 \), where 'a', 'b', and 'c' are coefficients. The task is to rewrite the quadratic equation as a product of two binomials.

For instance, in the equation \( y^2 - y - 2 = 0 \), the goal is to express it as \( (y - m)(y - n) = 0 \), where 'm' and 'n' are the solutions for 'y'. If the quadratic can be factored neatly, the solutions can quickly be determined by applying the zero product property, which states that if the product of two expressions is zero, at least one of the expressions must be zero. Hence, each binomial set equal to zero gives a solution to the quadratic equation. Factoring is usually the first choice for solving quadratic equations when possible because it is a straightforward method and often requires basic algebraic manipulation.

The substitution method is one of the techniques used to solve systems of equations. This method involves solving one of the equations for one variable in terms of others and then 'substituting' this into the other equations.

In the provided exercise, once we express 'x' from the first equation as \( x = y + 2 \), this expression for 'x' is substituted into the second equation, transforming it into a quadratic equation in one variable. This step effectively reduces the system of equations from two variables to one, simplifying the process of finding the solution set. With the given values of 'y' from the factored quadratic, we substitute back into the first equation to find the corresponding 'x' values. The substitution method is a powerful tool that can make complex systems of equations more manageable, especially when paired with factoring techniques as demonstrated in this exercise.