To find the solution to the system of equations:
[tex]\[
\left\{\begin{array}{l}
2x + 3y = -11 \\
y = x - 2
\end{array}\right.
\][/tex]
we can use the following steps:
1. Substitute [tex]\( y \)[/tex] from the second equation into the first equation:
Given [tex]\( y = x - 2 \)[/tex], we can substitute [tex]\( y \)[/tex] in the first equation:
[tex]\[
2x + 3(x - 2) = -11
\][/tex]
2. Simplify the equation:
Distribute the 3 on the left-hand side:
[tex]\[
2x + 3x - 6 = -11
\][/tex]
Combine like terms:
[tex]\[
5x - 6 = -11
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Add 6 to both sides of the equation to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
5x = -5
\][/tex]
Divide both sides by 5:
[tex]\[
x = -1
\][/tex]
4. Substitute [tex]\( x = -1 \)[/tex] back into the second equation to find [tex]\( y \)[/tex]:
Use the equation [tex]\( y = x - 2 \)[/tex]:
[tex]\[
y = -1 - 2 = -3
\][/tex]
So, the solution to the system of equations is:
[tex]\[
(x, y) = (-1, -3)
\][/tex]
Looking at the provided choices, the correct answer is:
[tex]\[
(-1, -3)
\][/tex]
