To solve the given system of linear equations:
[tex]\[
\begin{array}{l}
7x - 5y = 9 \\
-6x + 5y = -2
\end{array}
\][/tex]
we can use the method of elimination or substitution. Here, we will use the elimination method to find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
First, let's add the two equations together to eliminate [tex]\( y \)[/tex]:
[tex]\[
(7x - 5y) + (-6x + 5y) = 9 + (-2)
\][/tex]
Simplify:
[tex]\[
7x - 5y - 6x + 5y = 7
\][/tex]
Combine like terms:
[tex]\[
x = 7
\][/tex]
Now that we have [tex]\( x = 7 \)[/tex], we can substitute this value back into one of the original equations to solve for [tex]\( y \)[/tex]. Let's use the first equation:
[tex]\[
7(7) - 5y = 9
\][/tex]
Simplify the left-hand side:
[tex]\[
49 - 5y = 9
\][/tex]
Subtract 49 from both sides:
[tex]\[
-5y = 9 - 49
\][/tex]
[tex]\[
-5y = -40
\][/tex]
Divide both sides by -5:
[tex]\[
y = 8
\][/tex]
So, the solution to the system of equations is [tex]\( x = 7 \)[/tex] and [tex]\( y = 8 \)[/tex].
Therefore, the correct answer is:
(A) [tex]\( x = 7, y = 8 \)[/tex]
