Apply Cramer's Rule.
..... | 2 3 1 |
D= | 3 1 -4 | = 2(3-4)-3(9-16)+(-3+4)=-2+21+1=20
..... | -4 -1 3 |
...... | 12 3 1 |
Dx=| -5 1 -4 | = 12(3-4)-3(-15+24)+(5-6)=-12-27-1=-40
...... | 6 -1 3 |
...... | 2 12 1 |
Dy=| 3 -5 -4 | = 2(-15+24)-12(9-16)+(18-20)=18+84-2=100
...... | -4 6 3 |
...... | 2 3 12 |
Dz=| 3 1 -5 | = 2(6-5)-3(18-20)+12(-3+4)=2+6+12=20
...... | -4 -1 6 |
x=Dx/D=-40/20=-2; y=Dy/D=100/20=5; z=Dz/D=20/20=1.
CHECK: 2x+3y+z=-4+15+1=12; 3x+y-4z=-6+5-4=-5; -4x-y+3z=8-5+3=6. All OK! (x,y,z)=(-2,5,1).