SOLUTION: When my professor explains this I understand. When I get home, it is like written in Hebrew or something. Can you please explain to me (in detail) how to solve a problem like thi

Question 89878: When my professor explains this I understand. When I get home, it is like written in Hebrew or something. Can you please explain to me (in detail) how to solve a problem like this? I am trying to solve for (x,y,z). My final in is tomorrow and I need to know this stuff. Thanks in advance.
x+y+2z=11
x+y+3z=14
x+2y-z=5
Found 2 solutions by checkley75, scott8148:
Answer by checkley75(3666) (Show Source): You can put this solution on YOUR website!
x+y+2z=11 now subtract the second equation:
-(x+y+3z=14)
--------------------
-z=-3 or z=3 answer.
x+2y-3=5 now subtract the first equation after replacing z by 3:
-(x+y+2*3=11)
-----------------------------------
y-3+6=-6
y-3=0
y=3 answer.
x+3+2*3=11
x+3+6=11
x+9=11
x=11-9
x=2 answer.

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
first you take two pairs of equations and eliminate one of the variables

multiply third equation by 2 and add to first equation 2x+4y-2z+x+y+2z=10+11 ... 3x+5y=21 ... z is eliminated

multiply third equation by 3 and add to first equation 3x+6y-3z+x+y+3z=15+14 ... 4x+7y=29 ... z is eliminated

next, you take the pair of new equations and eliminate one of the variables

multiply first new equation by 4 and second new equation by -3 and add 12x+20y-12x-21y=84-87 ... -y=-3 ... y=3

take this value to one of the new equations to find x ... 3x+5(3)=21 ... x=2

take values of y and x to an original equation to find z ... 2+3+2z=11 ... z=3
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