To solve the system of equations
[tex]\[
\left\{\begin{array}{l}
2x + 3y = -11 \\
y = x - 2
\end{array}\right.
\][/tex]
we start by substituting the expression for [tex]\( y \)[/tex] from the second equation into the first equation.
Given:
[tex]\[ y = x - 2 \][/tex]
Substitute [tex]\( y \)[/tex] into the first equation:
[tex]\[ 2x + 3(x - 2) = -11 \][/tex]
Simplify the equation:
[tex]\[ 2x + 3x - 6 = -11 \][/tex]
[tex]\[ 5x - 6 = -11 \][/tex]
Add 6 to both sides:
[tex]\[ 5x = -11 + 6 \][/tex]
[tex]\[ 5x = -5 \][/tex]
Divide by 5:
[tex]\[ x = -1 \][/tex]
Now, substitute [tex]\( x \)[/tex] back into the second equation to find [tex]\( y \)[/tex]:
[tex]\[ y = x - 2 \][/tex]
[tex]\[ y = -1 - 2 \][/tex]
[tex]\[ y = -3 \][/tex]
Therefore, the solution to the system of equations is:
[tex]\[ (x, y) = (-1, -3) \][/tex]
So, the correct answer is:
[tex]\[ \boxed{(-1, -3)} \][/tex]
