Answer
$x=-4.57, \ y=-6.44, \ z=-24.07$
or $(-4.57, \ -6.44, \ -24.07)$
Work Step by Step
Writing the system in matrix form, $AX=B,$ the solution is $X=A^{-1}B$.
Here,
$A=\left[\begin{array}{rrr}{25}&{61}&{-12}\\{18}&{-2}&{4}\\{8}&{35}&{21}\end{array}\right]$, $B=\left[\begin{array}{l}
10\\
-9\\
12
\end{array}\right]$
Using desmos.com/matrix
select "New matrix", define the dimensions (3 by 3),
and enter the matrix entries for A.
Do the same for the (3 by 1) matrix B....
Enter $A^{-1}B$
(see screenshot)
we find $X\approx\left[\begin{array}{l}
-4.57\\
-6.44\\
-24.07
\end{array}\right]$
$x=-4.57, \ y=-6.44, \ z=-24.07$
or $(-4.57, \ -6.44, \ -24.07)$
