To solve the system of equations
[tex]\[
\begin{cases}
2x + 3y = 18 \\
3x + y = 6
\end{cases}
\][/tex]
we need to find values for [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that satisfy both equations simultaneously.
1. List the equations:
[tex]\[
2x + 3y = 18 \quad \text{(Equation 1)}
\][/tex]
[tex]\[
3x + y = 6 \quad \text{(Equation 2)}
\][/tex]
2. Solve Equation 2 for [tex]\(y\)[/tex]:
[tex]\[
3x + y = 6
\][/tex]
Subtract [tex]\(3x\)[/tex] from both sides to isolate [tex]\(y\)[/tex]:
[tex]\[
y = 6 - 3x
\][/tex]
3. Substitute [tex]\(y = 6 - 3x\)[/tex] into Equation 1:
[tex]\[
2x + 3(6 - 3x) = 18
\][/tex]
Simplify the equation:
[tex]\[
2x + 18 - 9x = 18
\][/tex]
Combine like terms:
[tex]\[
-7x + 18 = 18
\][/tex]
4. Isolate [tex]\(x\)[/tex]:
Subtract 18 from both sides:
[tex]\[
-7x = 0
\][/tex]
Divide by -7:
[tex]\[
x = 0
\][/tex]
5. Substitute [tex]\(x = 0\)[/tex] back into Equation 2 to find [tex]\(y\)[/tex]:
[tex]\[
3(0) + y = 6
\][/tex]
Simplify:
[tex]\[
y = 6
\][/tex]
Therefore, the solution to the system of equations is
[tex]\[
(x, y) = (0, 6)
\][/tex]
So the correct answer is:
[tex]\[
(0, 6)
\][/tex]
