The first equation, x^2 + y^2 = 34, signifies the sum of squares of x and y is 34. And the second equation, x^4 - y^4 = 544, where the fourth power of x is larger than that of y by 544. From the options, we have numbers and their negative counterparts. First, let`s exclude option 4 as sum of squares for 3 and 4 is 25, not 34. Next, option 1 and 3 can also be eliminated as their fourth power differences isn`t 544. So, we are left with option 2. Squaring 5 and 3 indeed gives us 34 and the difference between their fourth powers equals 544. Therefore, the correct answer is option 2 (+/-5, +/-3) because it rightly satisfies both the equations.