-x + y − z = 10 3x − 2y + 6z = 4 x + 2y + z = 5 (Eq1) + (Eq3) ⟶ (Eq3)

Answer 1

-x + y - z = 10

3x-2y + 6z = 4

x + 2y +z = 5

3*Eq1 + Eq2: y + 3z = 34

Eq1 + Eq2 : 3y = 15 --> y = 5

Substitutes:

5 + 3z = 34

3z = 29

z = 29/3

Per original first equation:

-x + y - z = 10

-x + 5 - 29/3 = 10

Multiplies by -3:

3x - 15 + 29 = -30

3x + 14 = -30

3x = -44

x = -44/3

the alleged solution is {x=-44/3, y = 5, z = 29/3}

check:

1st equation:

-x +y - z = -(-44/3) + 5 - 29/3 =

44/3 + 15/3 - 29/3 =

30/3 = 10, yes the first equation checks

2nd equation:

3x-2y + 6z =

3(-44/3) - 2(5) + 6(29/3) =

-44 - 10 + 58 = 4

so yes, the 2nd equation checks

x + 2y +z =

-44/3 + 2(5) + 29/3 =

-44/3 + 10 + 29/3 =

-15/3 + 10 =

-5 + 10 = 5

so yes the 3rd equation checks

the OFFICIAL solution is {x=-44/3, y = 5, z = 29/3}