Solve the system: x − y = 0.9 and 11/(x + y) = 2. Find the ordered pair (x, y).

Introduction / Context:
This is a two-equation system involving a linear equation and a reciprocal relation for the sum. It assesses equation-solving and substitution skills with decimals.

Given Data / Assumptions:

• x − y = 0.9
• 11/(x + y) = 2 ⇒ x + y = 11/2 = 5.5

Concept / Approach:
Solve the system formed by the sum and difference: x + y and x − y. Use the standard identities x = ( (x + y) + (x − y) ) / 2 and y = ( (x + y) − (x − y) ) / 2.

Step-by-Step Solution:

Verification / Alternative check:
Check: x − y = 3.2 − 2.3 = 0.9; 11/(x + y) = 11/5.5 = 2. Both satisfied.

Why Other Options Are Wrong:
The other choices do not satisfy both equations simultaneously; either the difference or the reciprocal sum fails.

Common Pitfalls:
Misreading 11/(x + y) as 11(x + y) or vice versa; sign errors; rounding intermediate results instead of keeping exact fractions/decimals.

Final Answer:
x = 3.2, y = 2.3