We have the following system of equations:
[tex]x+y+4z=6[/tex][tex]x+5y+2z=0[/tex][tex]x+8y-8z=-6[/tex]If we solve for x for the first equation we got:
[tex]x=6-y-4z\text{ (1)}[/tex]Now we can replace in the second equation and we got:
[tex]6-y-4z+5y+2z=0[/tex][tex]4y-2z=-6[/tex]And solving for y we got:
[tex]y=\frac{2z-6}{4}\text{ (2)}[/tex]Replacing the equations (1) and (2) into the final equation we got:
[tex]6-(\frac{2z-6}{4})-4z+8(\frac{2z-6}{4})-8z=-6[/tex][tex]6-\frac{z}{2}+\frac{3}{2}-4z+4z-12-8z=-6[/tex][tex]\frac{17}{2}z=6+6-12+\frac{3}{2}[/tex][tex]z=\frac{3}{17}[/tex]Now we can solve for y and x like this:
[tex]y=\frac{2(3/17)-6}{4}=-\frac{24}{17}[/tex][tex]x=6-(-\frac{24}{17})-4(\frac{3}{17})=\frac{114}{17}[/tex]And the final solution would be:
x= 114/17, y= -24/17, z= 3/17
