SOLUTION: Id have a question; does anyone know how to solve this system of equations? 3x+4y+z=7 2y+z=3 -5+3y+8z=-31 (the 2y is suppose to be listed under the 4y) could anyone explain

Question 207773: Id have a question; does anyone know how to solve this system of equations?
3x+4y+z=7
2y+z=3
-5+3y+8z=-31
(the 2y is suppose to be listed under the 4y) could anyone explain how this works??
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
3x+4y+z=7
2y+z=3
-5+3y+8z=-31
(the 2y is suppose to be listed under the 4y) could anyone explain how this works??
--------------
I'll assume you meant -5x in the 3rd line.
There are several ways to do these. One is elimination and substitution as follows:
3x+ 4y + z = 7 (x 5) --> 15x + 20y + 5z = 35
0x+ 2y + z = 3
-5x+3y + 8z= -31 (x3)--> -15x+ 9y + 24z = -93
-------------
Since there's no x in the 2nd line, eliminate x in one of the other 2.
15x + 20y + 5z = 35
-15x+ 9y + 24z = -93
--------------------- Add
0x + 29y + 29z = -58
y + z = -2
2y+ z = 3 2nd equation
--------- Subtract
-y = -5
y = 5
------ Then sub for y into y+z = -2
z = -7
-------- Sub for y and z into 3x+4y+z=7
x = -2
-----------
-----------
Another method uses determinants.
3x+ 4y + z = 7
0x+ 2y + z = 3
-5x+3y + 8z= -31
|+x y z 1|
|+3 4 1 7|
|+0 2 1 3| = 0
|-5 2 1 3|
I made an Excel sheet that solves those, and there are sites online that do them up to 10x10, too.
If you're interested, email me via the thank you note.

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