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Solve the following system by using substitution.

[tex]\[
\begin{aligned}
5x + y &= 24 \\
y &= 3x
\end{aligned}
\][/tex]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The solution set is [tex]\(\boxed{\ }\)[/tex]. (Type an ordered pair.)
B. There are infinitely many solutions.
C. The solution is the empty set.


Sagot :

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].