Respuesta :
The given system is:
[tex]\begin{gathered} 2x+y-3z=1\ldots(i) \\ 3x-y-4z=7\ldots(ii) \\ 5x+2y-6z=5\ldots(iii) \end{gathered}[/tex]Add (i) and (ii) to get:
[tex]\begin{gathered} 2x+y-3z=1 \\ + \\ 3x-y-4z=7 \\ 5x-7z=8\ldots(iv) \end{gathered}[/tex]Multiply (ii) by 2 to get:
[tex]6x-2y-8z=14\ldots(v)[/tex]Add (iii) and (v) to get:
[tex]\begin{gathered} 6x-2y-8z=14 \\ + \\ 5x+2y-6z=5 \\ 11x-14z=19\ldots(vi) \end{gathered}[/tex]Multiply (iv) by 2 to get:
[tex]10x-14z=16\ldots(vii)[/tex]Subtract (vii) from (vi) to get:
[tex]\begin{gathered} 11x-14z=19 \\ - \\ 10x-14z=16 \\ x=3 \end{gathered}[/tex]Put x=3 in (iv) to get:
[tex]\begin{gathered} 5\times3-7z=8 \\ -7z=8-15 \\ -7z=-7 \\ z=1 \end{gathered}[/tex]Put x=3 and z=1 in (i) to get:
[tex]\begin{gathered} 2(3)+y-3(1)=1 \\ 6+y-3=1 \\ y+3=1 \\ y=-2 \end{gathered}[/tex]So the values are x=3,y=-2 and z=1.
