What ordered pair (x, y) satisfies the system of linear equations 4x - 3y = 47 and 3x + y = 32?

Introduction / Context:
This problem checks your ability to solve a system of two linear equations in two variables and then identify the correct ordered pair from the options. Such systems are common in aptitude and algebra tests and can be solved using substitution or elimination methods. Here, the system 4x - 3y = 47 and 3x + y = 32 is straightforward to solve accurately.

Given Data / Assumptions:

• Equation 1: 4x - 3y = 47.
• Equation 2: 3x + y = 32.
• The pair (x, y) must satisfy both equations simultaneously.

Concept / Approach:
A simple method is to solve one equation for one variable and substitute into the other. Equation 2 is easy to rearrange for y. Substituting this expression into Equation 1 gives a single equation in x. After solving for x, we can find y and then match the ordered pair with the correct option.

Step-by-Step Solution:

Verification / Alternative check:
Check the solution in both equations. For Equation 1: 4*11 - 3*(-1) = 44 + 3 = 47, which is correct. For Equation 2: 3*11 + (-1) = 33 - 1 = 32, which matches the equation exactly. Since both equations are satisfied, the solution is confirmed.

Why Other Options Are Wrong:

Common Pitfalls:
Typical mistakes include algebraic errors when distributing negative signs, incorrect addition of constants, or mixing up the x and y values when checking solutions. Writing each substitution step clearly and checking with both equations helps eliminate these errors and ensures the pair is truly a common solution.

Final Answer:
{(11, -1)}