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Question 331405: solve the system x+y+z=-1
x-y+3z=-17
2x+y+z=-2
Answer by mathmandotcom(31)   (Show Source):
You can put this solution on YOUR website! three equations and three unknows x,y,z
1) x+y+z=1
2) x-y+3z=17 Lets take equation 1 and 2 then eliminate y by adding
3) 2x+y+z=-2 1) x+y+z=1
2) x-y+3z=17 adding we get equation 4) 2x+4z=18
next take eq 2 and 3 and eliminate the same variable y
2) x-y+3z=17
3) 2x+y+z=-2 adding we get eq 5)3x+4z=15
2x+4z=18 and 3x+4z=15 multiply eq 4) by -1 and add
-2x-4z=-18
3x+4z=15 adding we get -2x+3x-4z+4z=-18+15......x=-3 plug -3 in eq 4
2*-3+4z=18...-6+4z=18 solve for z by adding 6 then divide by 4
4z=24.........z=6 finialy use x=-3 asnd z=6 and plug into eq 1)
-3+y+6=1......y+3=1........y=-2 so we get (-3,-2,6) plug these into eq 1)
-3-2+6=1 to check 1=1 your solution is (-3,-2,6)
I hope this is not to crowed, good luck!
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