Solve the system of equations.

[tex]\[
\begin{array}{l}
2x + 3y = 18 \\
3x + y = 6
\end{array}
\][/tex]

A. [tex]\((9, 0)\)[/tex]

B. [tex]\((3, 4)\)[/tex]

C. [tex]\((1, 3)\)[/tex]

D. [tex]\((0, 6)\)[/tex]



Answer :

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]