Question

3x + 2y + z = 8 2x - 3y + 2z = -16 x + 4y - z = 20

Answer 1

I'll do a similar problem, and I challenge you to do this on your own using similar methods!

x+5y+2z=23
8x+4y+3z=12
9x-3y-7z=-10

Multiplying the first equation by -8 and adding it to the second one (to get rid of the x) and also multiplying the first equation by -9 and adding the third one to get rid of the x there too, we end up with

-36y-13z=-92
and
-48y-25z=-217

Multiplying both equations by -1, we get
36y+13z=-92
48y+25z=217

Multiplying the (new) first equation by -4/3 and adding it to the second (to get rid of the y), we get
(7+2/3)z=94+1/3

Dividing both sides by (7+2/3) to separate the z, we get
z=
`(282/3)/(23/3) = (282)/(23)`

Plugging that into
48y+25z=217, we can subtract 25z from both sides and divide by 48 to get

`y= (217-25z)/(48) =(217-25*282/23)/(48)`

Lastly, we plug this into x+5y+2z=23 to get
x=23-5y-2z by subtracting 5y+2z from both sides to get

`x=23- (217-25*282/23)/(48)*5-2*282/23`

Good luck, and feel free to ask with any questions!