Final answer:
After testing each of the given options in the system of equations, option A: x = 4, y = 8 is the only set of values that satisfy both equations, making it the correct solution.
Step-by-step explanation:
To determine which set of values is a solution to the given system of linear equations, we need to check which option satisfies both equations simultaneously:
Equations:
4x + y = 24
x - y = -4
We can substitute the given values from the options into the equations and check:
- For option A (x = 4, y = 8), the first equation gives us 4(4) + 8 = 24, which is true, and the second one gives us 4 - 8 = -4, which is also true. Hence, option A satisfies both equations.
- For option B (x = 2, y = 6), the first equation gives us 4(2) + 6 = 14, which is not 24, so it is not true for the first equation. Therefore, B is not a solution.
- For option C (x = 1, y = 1), the first equation gives us 4(1) + 1 = 5, which is not 24, so it is not true for the first equation. Thus, C is not a solution.
- For option D (x = 5, y = 4), the first equation gives us 4(5) + 4 = 24, which is true, but the second one gives us 5 - 4 = 1, which is not -4. Hence, D does not satisfy both equations either.
Therefore, the correct solution is option A: x = 4, y = 8.