Question

Resolva o sistema pela regra de cramer 2x-y+z=3
x+y+z=6
x-y+2z=3

Answer 1

Descobrindo o "valor" de Y:
y + z = 3..........y = - z + 3

Descobrindo o valor de X:
x + y + z = 6
x - z + 3 + z = 6
x = 6 - 3
x = 3

Descobrindo o valor de Z:
x - y + 2z = 3
3 + z - 3 + 2z = 3
3z = 3 + 3 - 3
3z = 3
z = 3/3
z = 1

Descobrindo o valor real de Y:
y + z = 3
y + 1 = 3
y = 3 - 1
y = 2

Answer 2

[2x-y+z=3
[x+y+z=6
[x-y+2z=3
[2. -1. 1]. 2. -1
[1. 1. 1]. 1. 1
[1. -1. 2]. 1. -1
D=4-1-1-1+2+2
D=4-3+4
D=4+1
D=5
∆x=[3. -1. 1]. 3. -1
[6. 1. 1]. 6. 1
[3. -1. 2]. 3. -1
∆x=-3-1-6-3+3+12
∆x=-13+15
∆x=2
∆y=[2. 3. 1]. 2. 3
[1. 6. 1]. 1. 6
[1. 3. 2]. 1. 3
∆y=24+3+3-6-6-6
∆y=24+6-18
∆y=24-12
∆y=12
∆z=[2. -1. 3]. 2. -1
[1. 1. 6]. 1. 1
[1. -1. 3]. 1. -1
∆z=6-6-3-3+12+3
∆z=-6+15
∆z=9
∆x/∆= 2/5
∆y/∆=12/5
∆z/∆=9/5
S={x=2/5, y=12/5, z=9/5}