Using Cramer's Rule:
Create determinant from coefficients, we'll call D=
| 2 -3 0 |
| 0 2 4 |
| 1 0 -5 |
Evaluate: 2(-10)+3(-4)=-20-12=-32.
Create determinate D[R1] from coefficients and constants:
| 7 -3 0 |
| 6 2 4 |
| -3 0 -5 |
Evaluate, D[R1]=7(-10)+3(-18)=-124.
D[R2]:
| 2 7 0 |
| 0 6 4 |
| 1 -3 -5 |
D[R2]=2(-18)-7(-4)=-8.
D[R3]:
| 2 -3 7 |
| 0 2 6 |
| 1 0 -3 |
D[R3]=2(-6)+3(-6)+7(-2)=-44.
R1=D[R1]/D=-124/-32=31/8; (also R2=D[R2]/D=-8/-32=1/4; R3=D[R3]/D=-44/-32=11/8).
CHECK
2(31/8)-3/4=28/4=7. OK
2(1/4)+4(11/8)=6. OK
31/8-55/8=-24/8=-3. OK