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Question 471075: Solve the system of equations
3x+4y+z=7
2y+z=3
-5x+3y+8z=-31
Answer by lwsshak3(11628)   (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
**
1) 3x+4y+z=7
2) 2y+z=3
3) -5x+3y+8z=-31
..
1) 3x+4y+z=7
2) 2y+z=3
4) 3x+2y=4 (subtract eq 2 from eq 1, eliminating z)
..
5) 24x+32y+8z=56 (multiply eq 1 by 8)
3) -5x+3y+8z=-31
6) 29x+29y=87 (subtract eq 3 from eq 5, eliminating z)
4) 3x+2y=4
..
7) 58x+58y=174 (multiply eq 6 by 2)
8) 87x+58y=116 (multiply eq 4 by 29)
9) -29x=58 (subtract eq 8 from eq 7, eliminating y)
x=-2
..
4) 3x+2y=4
2y=4-3x=4+6=10
y=5
..
3) -5x+3y+8z=-31
10+15+8z=-31
8z=-31-25=-56
z=-7
..
Check:
1) 3x+4y+z=3(-2)+4(5)-7=20-13=7
2) 2y+z=3=2(5)-7=3
3) -5x+3y+8z=-5(-2)+3(5)+(8)(-7)=10+15-56=-56+25=-31
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