Final answer:
The solution to the system of equations (3x - 2y = 12) and (3x + 5y = 33) is found using elimination, resulting in the point (6,3), which is option B.
Step-by-step explanation:
To solve the system of equations using elimination, we look at the given equations (3x - 2y = 12) and (3x + 5y = 33). The goal is to eliminate one of the variables by combining the equations. We can do this by first multiplying the first equation by 5 and the second equation by 2, which gives us:
- 15x - 10y = 60
- 6x + 10y = 66
Next, we add the equations together to eliminate the y variable:
- 15x + 6x - 10y + 10y = 60 + 66
- 21x = 126
Dividing both sides by 21, we find that x = 6. Now, we can substitute x back into one of the original equations to find y. Using the first equation 3x - 2y = 12:
- 3(6) - 2y = 12
- 18 - 2y = 12
- -2y = -6
- y = 3
Therefore, the solution to the system of equations is (6,3), which corresponds to option B.