To use the elimination method to solve the given system of equations:
2x + 3y = 18
3x - 3y = 12
First, add the two equations together to eliminate the y variable:
(2x + 3y) + (3x - 3y) = 18 + 12
The y variables cancel each other out:
2x + 3x = 30
Combine the x terms:
5x = 30
Now, solve for x by dividing both sides by 5:
5x / 5 = 30 / 5
x = 6
Next, substitute the value of x back into either of the original equations to solve for y. We'll use the first equation:
2x + 3y = 18
2(6) + 3y = 18
12 + 3y = 18
Subtract 12 from both sides:
3y = 6
Now, divide both sides by 3 to solve for y:
3y / 3 = 6 / 3
y = 2
The solution to the system of equations is (x, y) = (6, 2), which corresponds to option D.