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

1 answer:

4 0

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= $\frac{282/3}{23/3} = \frac{282}{23}$

Plugging that into
48y+25z=217, we can subtract 25z from both sides and divide by 48 to get
$y= \frac{217-25z}{48} =\frac{217-25*282/23}{48}$

Lastly, we plug this into x+5y+2z=23 to get
x=23-5y-2z by subtracting 5y+2z from both sides to get
$x=23- \frac{217-25*282/23}{48}*5-2*282/23$

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

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