To solve the given system of equations:
[tex]\[
\begin{array}{l}
2x + y = 5 \\
x - y = 4
\end{array}
\][/tex]
We can start by solving one of the equations for one of the variables and then substitute it into the other equation. Let's work with the second equation to express [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex]:
[tex]\[ x - y = 4 \][/tex]
[tex]\[ x = y + 4 \][/tex]
Next, we substitute [tex]\( x = y + 4 \)[/tex] into the first equation:
[tex]\[ 2(y + 4) + y = 5 \][/tex]
Simplify this equation:
[tex]\[ 2y + 8 + y = 5 \][/tex]
[tex]\[ 3y + 8 = 5 \][/tex]
Subtract 8 from both sides to isolate the term with [tex]\( y \)[/tex]:
[tex]\[ 3y = 5 - 8 \][/tex]
[tex]\[ 3y = -3 \][/tex]
Divide by 3:
[tex]\[ y = -1 \][/tex]
Now that we have the value of [tex]\( y \)[/tex], substitute [tex]\( y = -1 \)[/tex] back into the expression [tex]\( x = y + 4 \)[/tex]:
[tex]\[ x = -1 + 4 \][/tex]
[tex]\[ x = 3 \][/tex]
Thus, the solution to the system of equations is:
[tex]\[ (x, y) = (3, -1) \][/tex]
So, the correct answer from the given options is:
[tex]\[
(3, -1)
\][/tex]
