What is the solution to the following system of equations?

[tex]\[
\begin{array}{l}
7x + 2y = 24 \\
8x + 2y = 30
\end{array}
\][/tex]

A. (6, -9)
B. (5, -1)
C. (-6, 4)
D. Infinitely Many



Answer :

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].