To solve the given system of linear equations:
[tex]\[
\begin{cases}
7x + 2y = 24 \\
8x + 2y = 30
\end{cases}
\][/tex]
we can use the method of elimination or substitution. Let's proceed with the elimination method to find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
1. Step 1: Subtract the equations.
First, we'll subtract the first equation from the second equation to eliminate [tex]\( y \)[/tex]:
[tex]\[
(8x + 2y) - (7x + 2y) = 30 - 24
\][/tex]
Simplifying this, we get:
[tex]\[
8x + 2y - 7x - 2y = 6
\][/tex]
Which reduces to:
[tex]\[
x = 6
\][/tex]
2. Step 2: Substitute [tex]\( x \)[/tex] value into one of the original equations.
Let's substitute [tex]\( x = 6 \)[/tex] back into the first equation [tex]\( 7x + 2y = 24 \)[/tex]:
[tex]\[
7(6) + 2y = 24
\][/tex]
Simplify and solve for [tex]\( y \)[/tex]:
[tex]\[
42 + 2y = 24
\][/tex]
Subtract 42 from both sides:
[tex]\[
2y = 24 - 42
\][/tex]
[tex]\[
2y = -18
\][/tex]
Divide by 2:
[tex]\[
y = -9
\][/tex]
Therefore, the solution to the system of equations is:
[tex]\[
(x, y) = (6, -9)
\][/tex]
Thus, the correct answer is [tex]\( \boxed{(6, -9)} \)[/tex].
