Solve[{x + y - z == 6,x + y == 3,x - 3 y + 2 z == 1}]
{x -> 4,y -> -1,z -> -3}
Solve[{ y + z == 5,3 x + 2 y - z == 4 ,x + z == 6}]
{x -> 2,y -> 1,z -> 4}