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Let the larger number be xx and the smaller number be yy. The problem gives two linear equations: x+y=26x + y = 26 (sum) and x−y=8x - y = 8 (difference). Add the equations to eliminate yy: (x+y)+(x−y)=26+8⇒2x=34(x + y) + (x - y) = 26 + 8 \Rightarrow 2x = 34. Divide both sides by 2 to isolate xx: x=17x = 17. Substituting back to check: if x=17x = 17, then y=26−17=9y = 26 - 17 = 9. Verify the difference: 17−9=817 - 9 = 8, which matches the given condition. Therefore, the larger number is 17 (Option C). This classic system can also be solved by averaging: when you know sum and difference, the larger number is (sum+difference)/2=(26+8)/2=17(\text{sum} + \text{difference})/2 = (26 + 8)/2 = 17; the smaller is (sum−difference)/2=(26−8)/2=9(\text{sum} - \text{difference})/2 = (26 - 8)/2 = 9. On the GED, recognizing structures like “sum and difference” speeds problem solving: use elimination, substitution, or mental arithmetic with averages. Always perform a quick check by plugging values back into both conditions to avoid simple sign or arithmetic errors.