x={x1,x2,x3,x4,x5,x6,x7,x8}
a={{-5.14,16.63,9.76,-10.68,18.98,11.21,-8.18,-14.64},{0,12.86,-19.17,-4.47,9.21,18.14,-8.82,-5.52},{0,0,7.15,1.64,15.22,-18.16,0.74,16.85}, {0,0,0,7.88,-11.81,4.11,-15.58,1.28}, {0,0,0,0,9.97,-15.84,17.94,-8.24},{0,0,0,0,0,19.49,-5.53,-14.92},{0,0,0,0,0,0,-9.07,3.96},  {0,0,0,0,0,0,0,5.25} }
b={-16.78,19.74,-10.51,18.07,1.57,-15.48,-12.35,-2.67}

x={x1,x2,x3,x4,x5,x6,x7,x8}
a={{-5,16,9,-10,18,30,-8,-14},{0,12,-19,-4,9,18,-8,-5},{0,0,7,1,15,-18,0,16}, {0,0,0,7,-11,4,-15,1}, {0,0,0,0,9,-15,8,-8},{0,0,0,0,0,9,-5,-14},{0,0,0,0,0,0,-9,3},  {0,0,0,0,0,0,0,5} }
b={12,-10,-16,-48,-1,-87,-60,20}

sol=Solve[a.x==b,x]

solxi=x/.sol[[1]]//N

a.solxi

a.solxi==b

a//MatrixForm

b//MatrixForm

x//MatrixForm