Question 143785: Solve the following system of equations for the unknown variables.
3x + 3y = 3
-3x – 2z = -11
y + z = -1
Answer by nabla(475)   (Show Source):
You can put this solution on YOUR website! 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
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