$1.$ Save Baby Yoda! $(8$ points$)$

Despite our best efforts, we have lost Baby Yoda to former agents of the Galactic Empire. Luckily we were able to conceal a receiver in his locket, so now it's time to save Baby Yoda using our $16$A knowledge!

Baby Yoda has been delivered to an Imperial Star Destroyer. Rebel intel has provided us with access to their internal communication beacons. The ship's layout is $2-$dimensional with $3$ beacon locations specified in Table $1.$

Table $1$: Data from Destroyer Beacons and their coordinates.

Figure $1$: Diagram of the Destroyer's floor$-$plan with Beacon coordinates marked accordingly.

Explicitly write out a linear system of equations $($in matrix$-$vector form$)$ using the data above for finding Baby Yoda's location $\backslash (\backslash$vec$\{$x$\}=\backslash$left$[\backslash$begin$\{$array$\}\{$l$\}$x $\backslash \backslash$ y$\backslash$end$\{$array$\}\backslash$right$]\backslash ).$ Draw a box around your final linear system, then solve for Baby Yoda's location. Nonlinear terms are not permitted in your final system of equations. You must provide both the system and the location for full credit.