Final answer:
The correct solution to the system of equations is x = 3, y = 0.
Step-by-step explanation:
The correct solution to the system of equations is option B) x = 3, y = 0.
To solve the system, we can either use the substitution method or the elimination method. Let's use the elimination method:
Multiply the second equation by 2 to make the y's terms cancel each other out:
6x - 2y = 6
Next, subtract the first equation from the modified second equation:
(6x - 2y) - (3x + 2y) = 6 - 12
Simplify the equation:
3x - 4y = -6
Now, we have a new system of equations:
3x + 2y = 12
3x - 4y = -6
By adding the two equations together, the y terms will cancel out:
(3x + 2y) + (3x - 4y) = 12 - 6
Simplify the equation:
6x - 2y = 6
Now, divide each term by 2 to get:
3x - y = 3
Both equations are the same as the original system. Since the equations are equivalent, the solution is the same as well, which is x = 3 and y = 0.