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Solve the following system by using substitution:

[tex]\[
\begin{array}{r}
5x + y = 28 \\
y = 2x
\end{array}
\][/tex]

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

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

Sagot :

GinnyAnsweridn
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].
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