To solve the given system of linear equations:
[tex]\[
\begin{array}{l}
x + y = -2 \\
2x - 3y = -9
\end{array}
\][/tex]
Follow these steps in the correct sequence:
1. Substitute the value of [tex]\( x \)[/tex] from the first equation [tex]\( (x + y = -2) \)[/tex] to solve for [tex]\( y \)[/tex].
2. Solve for [tex]\( y \)[/tex].
3. The solution for the system of equations is [tex]\((-3, 1)\)[/tex].
Now, let's substitute the steps:
1. Substitute the value of [tex]\( x \)[/tex] from the first equation [tex]\( (x + y = -2) \)[/tex] to solve for [tex]\( y \)[/tex]:
[tex]\[
x = -2 - y
\][/tex]
2. Substitute [tex]\( x = -2 - y \)[/tex] into the second equation [tex]\( (2x - 3y = -9) \)[/tex]:
[tex]\[
2(-2 - y) - 3y = -9
\][/tex]
Simplify and solve for [tex]\( y \)[/tex]:
[tex]\[
-4 - 2y - 3y = -9 \\
-5y - 4 = -9 \\
-5y = -5 \\
y = 1
\][/tex]
3. Substitute [tex]\( y = 1 \)[/tex] back into the first equation [tex]\( (x + 1 = -2) \)[/tex]:
[tex]\[
x + 1 = -2 \\
x = -2 - 1 \\
x = -3
\][/tex]
Thus, the solution for the system of equations is [tex]\( (x, y) = (-3, 1) \)[/tex].
So, the correct final step is:
- The solution for the system of equations is [tex]\((-3, 1)\)[/tex].
