Final answer:
After substituting x with 2 and y with -1 into each set of systems of equations, we find that option c) y = 4x - 9; y = x - 3 is the only system where both equations are satisfied and thus has the solution (2, -1).
Step-by-step explanation:
The student is asking which systems of equations has a solution of (2, -1). To find the answer, we substitute x with 2 and y with -1 in each system of equations and see if both equations are satisfied.
- Option a) y = 5; 5x + 4y = -20. Substituting y = -1, we immediately see that the first equation is not satisfied, hence this cannot be the correct system.
- Option b) x + 2y = 10; -4x - y = 2. Substituting x = 2 and y = -1 yields the equations 2 - 2 = 10 and -8 + 1 = 2, neither of which are true, hence this is not the correct system.
- Option c) y = 4x - 9; y = x - 3. Substituting x = 2 into the first equation yields y = 8 - 9 = -1, and into the second equation yields y = 2 - 3 = -1. Both equations are satisfied, so this is the correct system.
- Option d) 0 = -2y + 10 - 6x; 14 - 22y = 18x. Substituting x = 2 and y = -1 into these equations results in incorrect identities, so this is not the correct system.
Therefore, the correct answer is option c) y = 4x - 9; y = x - 3.