Final answer:
The ordered pair (3, -1) satisfies both systems (b) and (c), meaning that it is a solution for both linear systems. The options provided were incomplete as the correct answer includes two applicable systems.
Step-by-step explanation:
To determine which linear system the ordered pair (3, -1) is a solution to, we need to plug the values of x and y into each system and see if the equations hold true. Let's substitute x with 3 and y with -1 in each system.
- For system (a), (2x - 5y = 11) and (x + 3y = 15), we get (2*3 - 5*(-1) = 11) and (3 + 3*(-1) = 15), which simplifies to (6 + 5 = 11) and (3 - 3 = 15). Clearly, the second equation does not hold true, so (a) is not the correct system.
- For system (b), (x + 2y = 1) and (-x + y = 2), we get (3 + 2*(-1) = 1) and (-3 + (-1) = 2), which simplifies to (3 - 2 = 1) and (-3 - 1 = 2). Both equations hold true, so (b) is the correct system.
- For system (c), (2x + 4y = 2) and (3x + y = 8), we get (2*3 + 4*(-1) = 2) and (3*3 + (-1) = 8), which simplifies to (6 - 4 = 2) and (9 - 1 = 8). Both equations hold true, so (c) is also a correct system.
- Therefore, system (d), 'None of the above,' is not the correct answer.
After evaluating the given systems, it turns out that both systems (b) and (c) are correct answers, making our initial options incomplete. The ordered pair (3, -1) is indeed a solution to both systems (b) and (c).