SOLUTION: Solve the system of equations 3x+4y+z=7 2y+z=3 -5x+3y+8z=-31 Please Help

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Question 922594: Solve the system of equations
3x+4y+z=7
2y+z=3
-5x+3y+8z=-31
Please Help
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

3x%2B4y%2Bz=7......eq.1
2y%2Bz=3.........eq.2
-5x%2B3y%2B8z=-31......eq.3
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+2y%2Bz=3......eq.2 ...solve for z
z=3-+2y

3x%2B4y%2Bz=7......eq.1...plug in z
3x%2B4y%2B3-2y=7
3x%2B2y=7-3
3x%2B2y=4......solve for x
3x=4-2y
x=4%2F3-2y%2F3

-5x%2B3y%2B8z=-31......eq.3..plug in z and x
-5%284%2F3-2y%2F3%29%2B3y%2B8%283-+2y%29=-31...solve for y
-20%2F3%2B10y%2F3%2B3y%2B24-+16y=-31...both sides multiply by 3
-20%2B10y%2B9y%2B72-+48y=-93
19y-48y=-93%2B20-72
-29y=-145.....both sides multiply by -1

29y=145
y=145%2F29
highlight%28y=5%29
go to z=3-+2y plug in y

z=3-+2%2A5
z=3-+10
highlight%28z=-7%29
go to x=4%2F3-2y%2F3 plug in y
x=4%2F3-%282%2A5%29%2F3
x=4%2F3-10%2F3
x=-6%2F3
highlight%28x=-2%29

so, highlight%28x=-2%29, highlight%28y=5%29, and highlight%28z=-7%29

check:
3x%2B4y%2Bz=7......eq.1
3%28-2%29%2B4%2A5%2B%28-7%29=7
-6%2B20-7=7
20-13=7
7=7