Derrick adds equations a and b to solve this system of equations. what makes this approach a valid method in general for solving a system of equations?

  The substitution and addition properties of equality.

Step-by-step explanation:

The substitution property tells you that equals may be substituted for each other at any time.

The addition property of equality tells you that the same quantity can be added to both sides of an equation without violating the equal sign.

So, if you start with the equation ...

  a = b

and you add c to both sides (addition property), you get

  a + c = b + c

and if c = d, this can become (substitution property) ...

  a + c = b + d . . . . . d substituted for c

In other words, we have added the equations

  a = b

  c = d

to get ...

  a + c = b + d

The addition and substitution properties of equality make this valid.