Don't immediately dive into algebra, substituting one equation into the next in a complicated cascade to try to get down to one variable. You can solve this way—but you'll need so many steps that you're a lot more likely to make mistakes (not to mention, waste a bunch of time).
Take a deep breath and examine this setup before you start trying to solve. The problem asks for x + y + z. There are three equations. It's a pain to try to combine just two of the equations (for example, if you subtract the second equation from the first one, you'll get the x to drop out...but you'll still be left with the two variables y and z).
Treat this as a Combo (short for combination of variables) problem. Is there a way to solve directly for x + y + z, all at once?
You need to end up with the same number of x's and y's and z's in the mix and they need to be added together. Across all three equations combined, there are a total of two x's, two y's, and two z's—that is, the same number of x's and y's and z's, exactly what you need. Try adding up all three equations at once. What happens?
2x + 2y + 2z = 26
x + y + z = 13
Done! The correct answer is (C).
The test writers are looking for ways to test your ability to think critically and logically about quant topics. Start building a habit of actually thinking about what the problem has given you and what it's asking you to find—before you start frantically doing a bunch of textbook algebra.
