Answer
\[
\vec{v}=\langle 7,-11\rangle \text { , } \vec{u}=\langle-5,8\rangle
\]
Work Step by Step
There are equations:
\[
\begin{array}{c}
\vec{v}+\vec{u}=\langle 2,-3\rangle \\
2 \vec{v}+3 \vec{u}=\langle-1,2\rangle
\end{array}
\]
where $\vec{u}$ and $\vec{v}$ are vectors.
From our first equation, we have that:
\[
-\vec{u}+\langle 2,-3\rangle=\vec{v}
\]
\[
\begin{aligned}
2 \vec{v}+3 \vec{u}=\langle-1,2\rangle & \Rightarrow 3 \vec{u}+2(\langle 2,-3\rangle-\vec{u})=\langle-1,2\rangle \\
& \Rightarrow 3 \vec{u}+\langle 4,-6\rangle-2 \vec{u}=\langle-1,2\rangle \\
& \Rightarrow \vec{u}=-\langle 4,-6\rangle+\langle-1,2\rangle \\
& \Rightarrow \vec{u}=\langle-5,8\rangle
\end{aligned}
\]
Since $\vec{v}=\langle 2,-3\rangle-\vec{u}$, we get:
\[
\vec{v}=-\langle-5,8\rangle+\langle 2,-3\rangle=\langle 7,-11\rangle
\]
Finally:
\[
\vec{v}=\langle 7,-11\rangle\text { , } \vec{u}=\langle-5,8\rangle
\]
