Answer:
The point is
.
Step-by-step explanation:
Given:
The set of equations are:
![x+y-z=-1\\4x-3y+2z=16\\2x-2y-3z=5](https://tex.z-dn.net/?f=x%2By-z%3D-1%5C%5C4x-3y%2B2z%3D16%5C%5C2x-2y-3z%3D5)
Multiply equation 1 by 2, we get
----- 4
Add equations 3 and 4.
![2x-2y-3z=5\\2x+2y-2z=-2\\](https://tex.z-dn.net/?f=2x-2y-3z%3D5%5C%5C2x%2B2y-2z%3D-2%5C%5C)
![(2x+2x)+(-2z-3z)=-2+5\\4x-5z=3](https://tex.z-dn.net/?f=%282x%2B2x%29%2B%28-2z-3z%29%3D-2%2B5%5C%5C4x-5z%3D3%20)
So, we got a new equation as
-------- 5
Now, we multiply equation 1 by 3, we get
![(x+y-z=-1)\times 3=3x+3y-3z=-3](https://tex.z-dn.net/?f=%28x%2By-z%3D-1%29%5Ctimes%203%3D3x%2B3y-3z%3D-3)
Now, add the following equations:
![3x+3y-3z=-3\\4x-3y+2z=16](https://tex.z-dn.net/?f=3x%2B3y-3z%3D-3%5C%5C4x-3y%2B2z%3D16)
This gives,
![(3x+4x)+(-3z+2z)=-3+16\\7x-z=13](https://tex.z-dn.net/?f=%283x%2B4x%29%2B%28-3z%2B2z%29%3D-3%2B16%5C%5C7x-z%3D13)
We got another new equation as
------- 6
Now, we multiply equation 6 by -5, we get
Now, we add the above equation and equation 5:
![-35x+5z=-65\\4x-5z=3](https://tex.z-dn.net/?f=-35x%2B5z%3D-65%5C%5C4x-5z%3D3)
![(-35x+4x)=-65+3\\-31x=-62\\x=\frac{-62}{-31}=2](https://tex.z-dn.net/?f=%28-35x%2B4x%29%3D-65%2B3%5C%5C-31x%3D-62%5C%5Cx%3D%5Cfrac%7B-62%7D%7B-31%7D%3D2)
Now, we plug in
in equation 6, we get
Now, we plug in
in equation 1, we get
![2+y-1=-1\\1+y=-1\\y=-1-1=-2](https://tex.z-dn.net/?f=2%2By-1%3D-1%5C%5C1%2By%3D-1%5C%5Cy%3D-1-1%3D-2)
Therefore, ![x=2,y=-2,z=1](https://tex.z-dn.net/?f=x%3D2%2Cy%3D-2%2Cz%3D1)
The point is ![(2,-2,1)](https://tex.z-dn.net/?f=%282%2C-2%2C1%29)