Answer
$x=4.56, \ y=-6.06, \ z=-22.55$
or $(4.56, \ -6.06, \ -22.55 )$
Work Step by Step
Writing the system in matrix form, $AX=B,$ the solution is $X=A^{-1}B$.
Here,
$A=\left[\begin{array}{rrr}{25}&{61}&{-12}\\{18}&{-2}&{4}\\{8}&{35}&{21}\end{array}\right], \quad B=\left[\begin{array}{l}
15\\
-3\\
12
\end{array}\right]$
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 $X\approx\left[\begin{array}{l}
4.56\\
-6.06\\
-22.55
\end{array}\right]$
$x=4.56, \ y=-6.06, \ z=-22.55$
or $(4.56, \ -6.06, \ -22.55 )$