Solve the following system of equations:

Question

x + 2y - z = 2
-3x + y + z = -9
x + y - 2z = 5

I came up with
(-2,-11/3, -2)
Is this correct?

Answer 1

No,
had you simply substituted your answer into the 1st equation, you would have seen that it was not correct

Add the 1st and 2nd ---> -2x+3y = -7 , (#4)
double the 2nd , then add to the 3rd ---> -5x +3y =-13 , (#5)

#4 - #5 :
3x = 6
x = 2

sub back into #4
-4 + 3y = -7
3y = -3
y = -1

back into 1st :
2 - 2 - z =2
-z = 2
z = -2

so (2,-1,-2)