To solve the system of equations using substitution, follow these steps:
1. Identify the system of equations:
[tex]\[
\begin{aligned}
5x + y &= 24 \quad \text{(Equation 1)} \\
y &= 3x \quad \text{(Equation 2)}
\end{aligned}
\][/tex]
2. Substitute Equation 2 into Equation 1:
Since [tex]\( y = 3x \)[/tex], we can replace [tex]\( y \)[/tex] in Equation 1 with [tex]\( 3x \)[/tex]:
[tex]\[
5x + (3x) = 24
\][/tex]
3. Combine like terms:
[tex]\[
5x + 3x = 8x
\][/tex]
[tex]\[
8x = 24
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{24}{8}
\][/tex]
[tex]\[
x = 3
\][/tex]
5. Substitute [tex]\( x = 3 \)[/tex] back into Equation 2 to find [tex]\( y \)[/tex]:
[tex]\[
y = 3x
\][/tex]
[tex]\[
y = 3(3)
\][/tex]
[tex]\[
y = 9
\][/tex]
So, the solution to the system of equations is the ordered pair [tex]\((3, 9)\)[/tex].
Therefore, the correct choice is:
A. The solution set is [tex]\(\{ (3, 9) \} \)[/tex].
