Make a determinant of the coefficients, Δ=
| -1 2 7 |
| 2 -1 -2 | = -1(-2+10)-2(4+6)+7(10+3)=--8-20+91=63
| 3 5 2 |
By replacing each variable column in turn with the constants for each row, we get Δx=
| 13 2 7 |
| -2 -1 -2 | = 13(-2+10)-2(-4-28)+7(-10-14)=104+64-168=0, x=Δx/Δ=0
| -14 5 2 |
Δy=
| -1 13 7 |
| 2 -2 -2 | = -1(-4-28)-13(4+6)+7(-28+6)=32-130-154=-252, y=Δy/Δ=-252/63=-4.
| 3 -14 2 |
Δz=
| -1 2 13 |
| 2 -1 -2 | = -1(14+10)-2(-28+6)+13(10+3)=-24+44+169=189, z=Δz/Δ=189/63=3.
| 3 5 -14 |
SOLUTION: x=0, y=-4, z=3.