To solve the system of equations using the elimination method, we perform the following steps:
Given:
[tex]\[
\begin{array}{l}
2x + 3y = 18 \quad \text{(1)} \\
3x - 3y = 12 \quad \text{(2)}
\end{array}
\][/tex]
Step 1: Eliminate [tex]\( y \)[/tex]
To eliminate [tex]\( y \)[/tex], we can add the two equations directly. Observe that in equation (2), the coefficient of [tex]\( y \)[/tex] is [tex]\(-3\)[/tex], which is the negative of the coefficient of [tex]\( y \)[/tex] in equation (1). Adding them will cancel out [tex]\( y \)[/tex].
So, add (1) and (2):
[tex]\[
(2x + 3y) + (3x - 3y) = 18 + 12
\][/tex]
Simplifying:
[tex]\[
2x + 3x + 3y - 3y = 30
\][/tex]
[tex]\[
5x = 30
\][/tex]
Dividing both sides by 5:
[tex]\[
x = 6
\][/tex]
Step 2: Substitute [tex]\( x = 6 \)[/tex] back into one of the original equations to find [tex]\( y \)[/tex]
We can use either equation (1) or (2). Let's use equation (1):
[tex]\[
2x + 3y = 18
\][/tex]
Substitute [tex]\( x = 6 \)[/tex]:
[tex]\[
2(6) + 3y = 18
\][/tex]
[tex]\[
12 + 3y = 18
\][/tex]
Subtract 12 from both sides:
[tex]\[
3y = 6
\][/tex]
Divide both sides by 3:
[tex]\[
y = 2
\][/tex]
Step 3: Write down the solution
The solution to the system of equations is [tex]\( (x, y) = (6, 2) \)[/tex].
So, the answer is:
[tex]\[
B. (6, 2)
\][/tex]
