Sure! Let's solve the given system of equations using the substitution method step by step.
The system of equations is:
[tex]\[
\begin{align*}
1. & \quad x + 2y = 14 \\
2. & \quad y = x + 4
\end{align*}
\][/tex]
Step 1: We have the second equation in terms of [tex]\( y \)[/tex]:
[tex]\[y = x + 4\][/tex]
Step 2: Substitute [tex]\( y \)[/tex] from the second equation into the first equation:
[tex]\[x + 2(x + 4) = 14\][/tex]
Step 3: Distribute and combine like terms:
[tex]\[x + 2x + 8 = 14\][/tex]
[tex]\[3x + 8 = 14\][/tex]
Step 4: Isolate [tex]\( x \)[/tex] by subtracting 8 from both sides:
[tex]\[3x = 6\][/tex]
Step 5: Divide both sides by 3 to find [tex]\( x \)[/tex]:
[tex]\[x = 2\][/tex]
Now that we have [tex]\( x \)[/tex], we can substitute it back into the second equation to find [tex]\( y \)[/tex]:
[tex]\[y = x + 4\][/tex]
[tex]\[y = 2 + 4\][/tex]
[tex]\[y = 6\][/tex]
So, the solution to the system of equations is the ordered pair [tex]\((x, y) = (2, 6)\)[/tex].
The correct answer is:
D. [tex]\((2, 6)\)[/tex]
