Answer
$x\approx-2.05, \ y\approx 3.88, \ z\approx 13.36$
or $(-2.05, \ 3.88, \ 13.36 )$
Work Step by Step
Writing the system in matrix form, $AX=B,$ the solution is $X=A^{-1}B$.
Here,
$A=\left[\begin{array}{rrr}{25}&{61}&{-12}\\{18}&{-2}&{4}\\{8}&{35}&{21}\end{array}\right], \quad B=\left[\begin{array}{l}
25\\
10\\
-4
\end{array}\right]$
Using desmos.com/matrix here:
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 $X\approx\left[\begin{array}{l}
-2.05\\
3.88\\
13.36
\end{array}\right]$
$x\approx-2.05, \ y\approx 3.88, \ z\approx 13.36$
or $(-2.05, \ 3.88, \ 13.36 )$