To solve the system of equations using substitution, we'll follow a step-by-step process:
Given the system:
[tex]\[
\begin{array}{r}
5x + y = 28 \\
y = 2x
\end{array}
\][/tex]
1. Substitute the expression for [tex]\( y \)[/tex] from the second equation into the first equation.
The second equation tells us that [tex]\( y = 2x \)[/tex]. We can substitute this into the first equation:
[tex]\[
5x + (2x) = 28
\][/tex]
2. Combine like terms and solve for [tex]\( x \)[/tex].
Combining the terms involving [tex]\( x \)[/tex]:
[tex]\[
5x + 2x = 28
\][/tex]
[tex]\[
7x = 28
\][/tex]
Now, solve for [tex]\( x \)[/tex] by dividing both sides by 7:
[tex]\[
x = \frac{28}{7}
\][/tex]
[tex]\[
x = 4
\][/tex]
3. Use the value of [tex]\( x \)[/tex] to find [tex]\( y \)[/tex].
We know from the second equation that [tex]\( y = 2x \)[/tex]. Substitute [tex]\( x = 4 \)[/tex]:
[tex]\[
y = 2 \times 4
\][/tex]
[tex]\[
y = 8
\][/tex]
4. Write the solution as an ordered pair.
The solution to the system of equations is the ordered pair [tex]\( (x, y) \)[/tex]:
[tex]\[
(4, 8)
\][/tex]
Therefore, the correct choice is:
A. The solution set is [tex]\(\{ (4, 8) \} \)[/tex].
