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apologiabiology

hmm
what you do is try to eliminate 1 variable in 2 equaions first
we can elminate x's in first and 2nd equation

add first and 2nd equation
x+3y-2z=10
-x-2y+z=-7 +
0x+y-z=3
y-z=3


multiply 2nd equation by 3 and add to last one
-3x-6y+3z=-21
3x+9y-5z=28 +
0x+3y-2z=7

3y-2z=7

we now have
y-z=3
3y-2z=7
multiply first equation by -2 and add to 2nd

-2y+2z=-6
3y-2z=7 +
y+0z=1
y=1

now we can sub back
y-z=3
1-z=3
minus 1
-z=2
times -1
z=-2

sub baack into any equation
x+3(1)-2(-2)=10
x+3+4=10
x+7=10
minus 7
x=3

x=3
y=1
z=-2
(3,1,-2)

Tucon


\(\displaystyle \\ ~~~~x+3y-2z=10 ~~~~~(E_1)\\ -x-2y+z=-7 ~~~~~(E_2)\\ ~~3x+9y-5z=28~~~~~(E_3) \\ \text{- - - - - } \\ E_1 + E_2 ~~\Longrightarrow~~y - z = 3 \\ \\ -3 \times E_1 + E3 ~~\Longrightarrow~~ z = -2 \\ \\ \Longrightarrow\Longrightarrow\Longrightarrow \\ \\ y-z=3\\ z = \boxed{-2}\\ \text{- - - - - }\\ y-(-2)=3\\ y+2=3\\ y =3-2=\boxed{1}\\ \text{- - - - - }\\ x+3y-2z=10\\ x+3\cdot 1-2\cdot (-2)=10\\ x+3+4=10\\ x+7=10\\ x= 10 - 7 = \boxed{3}\)



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