Question

x+2y-z=2 2x-y+z=3 x+y+z=6

Answer 1

{x+2y-z=2
{2x-y+z=3
{x+y+z=6
[1. 2. -1]. 1. 2
[2. -1. 1]. 2. -1
[1. 1. 1]. 1. 1
D=-1+2-2+1-1-4
D=-1-4
D=-5
∆x=[2. 2. -1] 2. 2
[3. -1. 1]. 3. -1
[6. 1. 1]. 6. 1
∆x=-2+12-3-6-2-6
∆x=-2-3-6-2-6+12
∆x=-19+12
∆x=-7
∆y=[1. 2. -1] 1. 2
[2. 3. 1] 2. 3
[1. 6. 1] 1. 6
∆y=3+2-12+3-6-4
∆y=3+2+3-12-6-4
∆y=8-22
∆y=-14
∆z=[1. 2. 2] 1. 2
[2 -1 3]. 2. -1
[1. 1 6]. 1. 1
∆z=-6+6+6+2-3-24
∆z=+6+2-3-24
∆z=+8-27
∆z=-19
∆x/∆=-7/-5
∆y/∆=-14/-5
∆z/∆=-19/-5