Answer:
D. (-10, -3), (-3, -10)
Step-by-step explanation:
For a question like this, it is easiest to check the offered answers in the given equations.
The first equation requires the sum of the x- and y-values to be -13. Adding two numbers is pretty easy, so you can rapidly determine that choice D is the only reasonable choice.
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<em>Comment on the process</em>
Answering multiple-choice questions is as much about test-taking skill as it is about math skill. First, you eliminate choices that don't answer the question.
Then you see if there is a way to identify the "correct" answer from the remaining "reasonable" answers. Often, that requires you only solve part of the problem, or you check for consistency between parts of the answer. (Here, if (a, b) is an answer, then (b, a) will be the other answer. Again, only choice D has that characteristic.)
You can see if the answer choices satisfy the details of the problem requirements.
Finally, <em>as a last resort</em>, you actually work the problem to determine your own answer to the question. (Here, you can substitute for y: x^2 +(-13-x)^2 = 109, then solve the quadratic, 2x^2 +26x +60 = 0 to find x=-3 or -10.) When you're done with this, you also need to <em>check your answer</em> against the above criteria.
