If 3(x − y) = 27 and 3(x + y) = 243, find x.

Given data

• 3(x − y) = 27 ⇒ x − y = 9.
• 3(x + y) = 243 ⇒ x + y = 81.

Concept / Approach

• Solve the system by adding to eliminate y.

Step-by-step calculation

(x − y) + (x + y) = 9 + 81 ⇒ 2x = 90 ⇒ x = 45.

Verification

Then y = 81 − 45 = 36. Check: x − y = 9 ✔.

Common pitfalls

• Dividing by 3 after already simplifying; double-counting factors.

Final Answer

45.