Question 143785
I'm going to solve this with matrices. You could solve this through substitution among other methods as well...
3   3   0   3
-3  0  -2  -11
0   1   1   -1

R1+R2--->

3   3   0   3
0   3  -2  -8
0   1   1  -1

1/3R1--->

1   1   0   1
0   3  -2  -8
0   1   1  -1

1/3R2-->
1   1   0     1
0   1  -2/3  -8/3
0   1   1    -1

-R2+R3-->
1   1   0       1
0   1  -2/3    -8/3
0   0   5/3     5/3

-R2+R1-->
1   0   2/3    11/3
0   1  -2/3    -8/3
0   0   5/3     5/3

3/5R3-->
1   0   2/3    11/3
0   1  -2/3    -8/3
0   0   1       1

2/3R3+R2-->
1   0   2/3    11/3
0   1   0      -2
0   0   1       1

-2/3R3+R1-->
1   0   0   3
0   1   0   -2
0   0   1   1

We can now read off the solution set:
{3,-2,1}.
check:
3(3) + 3(-2) = 9-6=3
-3(3) – 2(1) = -9-2=-11
-2 + 1 = -1