To solve the system of equations using the substitution method, follow these steps:
1. We are given the system of equations:
[tex]\[
\begin{cases}
2x + 4y = 14 \\
x = 3
\end{cases}
\][/tex]
2. Since the second equation already gives us the value of [tex]\( x \)[/tex], we can substitute this value into the first equation.
Substitute [tex]\( x = 3 \)[/tex] into the first equation:
[tex]\[
2(3) + 4y = 14
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
Simplify the left-hand side:
[tex]\[
6 + 4y = 14
\][/tex]
4. Isolate [tex]\( y \)[/tex] by subtracting 6 from both sides:
[tex]\[
4y = 14 - 6
\][/tex]
[tex]\[
4y = 8
\][/tex]
5. Divide both sides by 4 to solve for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{8}{4}
\][/tex]
[tex]\[
y = 2
\][/tex]
6. Therefore, the solution to the system of equations is [tex]\( x = 3 \)[/tex] and [tex]\( y = 2 \)[/tex]. This corresponds to the ordered pair [tex]\((3, 2)\)[/tex].
So, the correct answer is:
C. [tex]\((3, 2)\)[/tex]
