SOLUTION: Solve this system of linear equations using matrices. x + y = 3 2y = 10 3x + 2y - 4z = 12 ----------- ----------- ----------- The answer is (-2

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Question 633334: Solve this system of linear equations using matrices.
x + y = 3
2y = 10
3x + 2y - 4z = 12
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The answer is (-2, 5, 2); I want someone to walk me through this problem, because I'm just not able to solve it correctly using row operations. Here's my work:

------------------
1 1 0 3
0 2 0 10
3 2 -4 12
------------------
1 1 0 3
0 2/2 0 10/2
3 2 -4 12
------------------
1 1 0 3

0 1 0 5
-3(1)+3 -3(1)+2 -4 -3(3)+12
------------------
1 1 0 3
0 1 0 5
0 1(1)-1 -4 1(3)+3
------------------
1 1 0 3
0 1 0 5
0 0 -4/-4 6/-4
------------------
1 1 0 3
0 1 0 2
0 0 1 -6/4
------------------

I got z = -6/4, but it's supposed to equal 2... what am I doing wrong?
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
Actually the answer is -2, 5, -2 not -2, 5, 2
I don't know where you went wrong but after you found y=5
You could have gotten x=-2
1 1 0 3
0 1 0 5
1 0 0 -2
now we have
1 0 0-2
0 1 0 5
3 2 -4 12
3 0 0 -6
0 2 -4 18
0 2 0 10
0 0 -4 8
which leaves
0 0 1 -2