Sure, let's solve the system of equations using the substitution method.
Given the equations:
[tex]\[
\begin{array}{l}
y = 7x + 8 \quad \text{(Equation 1)} \\
y = x + 20 \quad \text{(Equation 2)}
\end{array}
\][/tex]
To solve this system, we will set the right sides of the equations equal to each other since both equations are equal to [tex]\( y \)[/tex].
So,
[tex]\[
7x + 8 = x + 20
\][/tex]
Next, we need to isolate [tex]\( x \)[/tex] by first eliminating [tex]\( x \)[/tex] from one side of the equation:
[tex]\[
7x + 8 - x = x + 20 - x
\][/tex]
This simplifies to:
[tex]\[
6x + 8 = 20
\][/tex]
Now, subtract 8 from both sides to further isolate [tex]\( x \)[/tex]:
[tex]\[
6x + 8 - 8 = 20 - 8
\][/tex]
This simplifies to:
[tex]\[
6x = 12
\][/tex]
Next, divide both sides by 6:
[tex]\[
x = \frac{12}{6}
\][/tex]
So,
[tex]\[
x = 2
\][/tex]
With [tex]\( x \)[/tex] found, substitute [tex]\( x = 2 \)[/tex] back into one of the original equations to solve for [tex]\( y \)[/tex]. Using Equation 1:
[tex]\[
y = 7x + 8
\][/tex]
Substitute [tex]\( x = 2 \)[/tex]:
[tex]\[
y = 7(2) + 8
\][/tex]
This simplifies to:
[tex]\[
y = 14 + 8
\][/tex]
So,
[tex]\[
y = 22
\][/tex]
The ordered pair that solves this system of equations is:
[tex]\[
(x, y) = (2, 22)
\][/tex]
Thus, the correct choice is:
A. [tex]\((2, 22)\)[/tex]
