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=[tex] \frac{282/3}{23/3} = \frac{282}{23} [/tex]
Plugging that into
48y+25z=217, we can subtract 25z from both sides and divide by 48 to get
[tex]y= \frac{217-25z}{48} =\frac{217-25*282/23}{48}[/tex]
Lastly, we plug this into x+5y+2z=23 to get
x=23-5y-2z by subtracting 5y+2z from both sides to get
[tex]x=23- \frac{217-25*282/23}{48}*5-2*282/23[/tex]
Good luck, and feel free to ask with any questions!
