SOLUTION: Write the system of linear equations in trian- gular form x + y + z = 7 3x + 4y + z = 13 2x − 2y + 9z = 7 What is triangular form and how would I solve this problem usin

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Write the system of linear equations in trian- gular form x + y + z = 7 3x + 4y + z = 13 2x − 2y + 9z = 7 What is triangular form and how would I solve this problem usin      Log On


   

Question 353410: Write the system of linear equations in trian-
gular form
x + y + z = 7
3x + 4y + z = 13
2x − 2y + 9z = 7
What is triangular form and how would I solve this problem using it?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
x + y + z = 7
3x + 4y + z = 13
2x − 2y + 9z = 7
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Subtract 3 times the 1st line from the 2nd line
Subtract 2 times the 1st line from the 3rd line
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x + y + z = 7
0 + y - 2z = -8
0 -4y + 7z = -7
----------------------
Add 4 times the 2nd line to the 3rd to get:
x + y + z = 7
0 + y - 2z = -8
0 + 0 - z = -39
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That is the triangle form (see the triangle of zeros in
the left bottom corner.
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Note that you can solve for "z" in the 3rd line z = 39
--
Then you can substiute 39 for "z" in the 2nd line and solve for y = 70.
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Then you can substitute for z and for y in the 1st line and solve for x=-102.
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Cheers,
Stan H.