To solve the given system of equations, we will use the method of substitution or elimination. Here are the steps to find the solution:
1. Write Down the Equations:
[tex]\[
\begin{cases}
2x + 3y = 18 & \text{...Equation (1)} \\
3x + y = 6 & \text{...Equation (2)}
\end{cases}
\][/tex]
2. Express y in Terms of x from Equation (2):
[tex]\[
3x + y = 6 \\
y = 6 - 3x
\][/tex]
3. Substitute y into Equation (1):
[tex]\[
2x + 3(6 - 3x) = 18 \\
2x + 18 - 9x = 18 \\
-7x + 18 = 18
\][/tex]
4. Solve for x:
[tex]\[
-7x = 0 \\
x = 0
\][/tex]
5. Substitute x Back into the Expression for y:
[tex]\[
y = 6 - 3(0) \\
y = 6
\][/tex]
After solving both equations, we find that the solution to the system of equations is:
[tex]\[
(x, y) = (0, 6)
\][/tex]
Therefore, the correct answer is:
[tex]\[
(0, 6)
\][/tex]
