To solve the system of equations using substitution, follow these steps:
1. Identify the system of equations:
[tex]\[
\begin{cases}
5x + y = 14 \quad \text{(Equation 1)} \\
y = 2x \quad \text{(Equation 2)}
\end{cases}
\][/tex]
2. Substitute [tex]\( y \)[/tex] from Equation 2 into Equation 1:
Since Equation 2 gives [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
[tex]\[
y = 2x
\][/tex]
Substitute [tex]\( y = 2x \)[/tex] into Equation 1:
[tex]\[
5x + 2x = 14
\][/tex]
3. Combine like terms and solve for [tex]\( x \)[/tex]:
[tex]\[
7x = 14
\][/tex]
Divide both sides by 7 to isolate [tex]\( x \)[/tex]:
[tex]\[
x = \frac{14}{7}
\][/tex]
[tex]\[
x = 2
\][/tex]
4. Substitute [tex]\( x = 2 \)[/tex] back into Equation 2 to find [tex]\( y \)[/tex]:
[tex]\[
y = 2x
\][/tex]
Substitute [tex]\( x = 2 \)[/tex]:
[tex]\[
y = 2 \cdot 2
\][/tex]
[tex]\[
y = 4
\][/tex]
5. Write the solution as an ordered pair:
The solution to the system of equations is:
[tex]\[
(x, y) = (2, 4)
\][/tex]
Therefore, the correct choice is:
A. The solution is [tex]\((2, 4)\)[/tex].
