Answer:
The point is [tex](2,-2,1)[/tex].
Step-by-step explanation:
Given:
The set of equations are:
[tex]x+y-z=-1\\4x-3y+2z=16\\2x-2y-3z=5[/tex]
Multiply equation 1 by 2, we get
[tex](x+y-z=-1)\times 2=2x+2y-2z=-2[/tex] ----- 4
Add equations 3 and 4.
[tex]2x-2y-3z=5\\2x+2y-2z=-2\\[/tex]
[tex](2x+2x)+(-2z-3z)=-2+5\\4x-5z=3 [/tex]
So, we got a new equation as [tex]4x-5z=3[/tex]-------- 5
Now, we multiply equation 1 by 3, we get
[tex](x+y-z=-1)\times 3=3x+3y-3z=-3[/tex]
Now, add the following equations:
[tex]3x+3y-3z=-3\\4x-3y+2z=16[/tex]
This gives,
[tex](3x+4x)+(-3z+2z)=-3+16\\7x-z=13[/tex]
We got another new equation as [tex]7x-z=13[/tex] ------- 6
Now, we multiply equation 6 by -5, we get
[tex](7x-z=13)\times -5=-35x+5z=-65[/tex]
Now, we add the above equation and equation 5:
[tex]-35x+5z=-65\\4x-5z=3[/tex]
[tex](-35x+4x)=-65+3\\-31x=-62\\x=\frac{-62}{-31}=2[/tex]
Now, we plug in [tex]x=2[/tex] in equation 6, we get
[tex]7\times 2-z=13\\14-z=13\\z=14-13=1[/tex]
Now, we plug in [tex]x=2,z=1[/tex] in equation 1, we get
[tex]2+y-1=-1\\1+y=-1\\y=-1-1=-2[/tex]
Therefore, [tex]x=2,y=-2,z=1[/tex]
The point is [tex](2,-2,1)[/tex]
