SOLUTION: solve the system of equations. 3x+4y+z=7 2y+z=3 -5x+3y+8z=-31 im not sure how to do this. i would greatly appreciate any help. thank you

Question 282372: solve the system of equations.
3x+4y+z=7
2y+z=3
-5x+3y+8z=-31 im not sure how to do this. i would greatly appreciate any help. thank you
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
solve the system of equations.
3x+4y+z=7
2y+z=3
-5x+3y+8z=-31
-----------------
There's more than one way, but I'll use substitution since there's no x term in the 2nd eqn.
--------------
2y+z=3 --> z = 3-2y
Sub for z in the other 2 eqns
3x + 4y + (3-2y) = 7
-5x + 3y +8(3-2y) = -31
----------------
3x + 2y = 4
-5x -13y = -55
Now it's 2 eqn in 2 variables.
Multiply the 1st by 5 and the 2nd by 3
15x + 10y = 20
-15x -39y = -165
---------------- Add
-29y = -145
y = 5
-------
Sub for y in 3x + 2y = 4
--> x = -2
-------------
2y+z=3
--> z = -7
-------------
If you're gonna do a lot of these, use Excel and determinants.

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