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ijhsj ijhsj
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10 years ago
i am having trouble with this three equation three variable problem. the equations are:
x+y+z=0
2x+3y+z=7
x-y+2z= -3
can anyone explain how to solve it, or just one variable. i think i can figure it out from there.
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#1
10 years ago
yes, you first eliminate one variable by substuting it into the other two equa.  note that
x = -y-z,   than put this into each other the other two equations
 2 (-y-z) + 3y + z = 7
(-y-z) - y +2z = -3

now multiply out each equation and then solve for either y or z.
that gives you the other one.
then using what y and z are, use the first equation to solve for x
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09mohamf09mohamf
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#2
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10 years ago
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#3
10 years ago
hmm this is a simple question.. : try this out :
x+y+x=0 Rightwards Arrow and Rightwards Arrow x-y+2z=-3    / + on the two equations..
we will have 2x+3z=-3 Rightwards Arrow 2x = -3 - 3z Rightwards Arrow x = (-3-3z)/2  this is first.. : second.. use the X..
1) x+y+z=0 / *3 Rightwards Arrow 3x+3y+3z=0 Rightwards Arrow and use the equation 2x +3y +z = 7 ......
now do - to the two.. it will be now.. : x+2z=0... , but remember that first you've known that x=(-3-3z)/2 ---> put it in the new equation which is x+2z=0...  
(-3-3z)/2 + 2z =0 --- > / *2 ---> -3-3z+4z=0 ---> -3+z=0 ---> z=3
here we know the Z ... now you can know the X.. by putting the Z=3 --- > x+2z=0 " we've figured it out before " , x+2*3 = 0 ---- > x=-6 ... and the why is simple.. from the first equation.. : x+y+z=0 ---> -6 + y + 3 = 0 ----> y=3 , FINAL ANSWER IS : x=-6 , y=3 , z=3  Wink Face
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#4
10 years ago
The simplest way to do it is to move one variable alone so, to solve for z, your three equations can become:
-(x+y)= z
7-(2x+3y)= z
(-3-(x-y))/2= z

then you just set all the equations equal to each other. Once you solve for one of the variables, you can just plug it in to teh equations and solve for th other ones (or repeat the method of setting the equations equal to each other)

therefore, you end up with

-x-y = 7-2x-3y = (-3-x+y)/2 = z
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