Solving the system of equations 3x - 6y = 24 and 6y = 42 - 8x using substitution yields the solution x = 6 and y = -1. This solution does not match any of the provided options, suggesting there might be a typo or error in the question.
To solve the simultaneous equations 3x - 6y = 24 and 6y = 42 - 8x, we can use the substitution method. First, we solve the second equation for y:
- 6y = 42 - 8x
- y = 7 - (4/3)x
Then we substitute this expression for y into the first equation:
- 3x - 6(7 - (4/3)x) = 24
- 3x - 42 + 8x = 24
- 11x = 66
- x = 6
Now that we have x, we can substitute it back into the equation for y:
- y = 7 - (4/3)(6)
- y = 7 - 8
- y = -1
So, the solution to the system of equations is x = 6 and y = -1, which is not listed among the options you provided. It's possible that there was a misunderstanding or a typo in the provided options.