Question

Observe el siguiente sistema 3x3 2x-y + 2z = 6 3x + 2y-z = 4 4x + 3y-3z = 1 la solución al sistema es

Answer 1

Respuesta:

$x=1\\y=2\\z=3$

Explicación paso a paso:

$2x-y+2z=6~~~~~.....(1)\\3x+2y-z=4~~~~~.....(2)\\4x+3y-3z=1~~~~~...(3)$

Eliminando $y$ en (1) y (2)                                 Eliminando $y$ en (1) y (3)

  $2x-y+2z=6\\3x+2y-z=4\\\\2(2x-y+2z)=2(6)\\3x+2y-z=4\\\\4x-2y+4z=12\\3x+2y-z=4\\\\7x+3z=16~~~~~.....(4)$                                         $2x-y+2z=6\\4x+3y-3z=1\\\\3(2x-y+2z)=3(6)\\4x+3y-3z=1\\\\6x-3y+6z=18\\4x+3y-3z=1\\\\10x+3z=19~~~~~.....(5)$

Eliminando $z$ en (4) y (5)

  $7x+3z=16\\10x+3z=19\\\\-(7x+3z)=-(16)\\10x+3z=19\\\\-7x-3z=-16\\10x+3z=19\\\\3x=3\\\\x=\frac{3}{3}\\\\x=1$

Hallando $z$ en (4)                                    Hallando $y$ en (2)

$7x+3z=16\\\\7(1)+3z=16\\\\7+3z=16\\\\3z=16-7\\\\z=\frac{9}{3}\\\\z=3$                                         $3x+2y-z=4\\\\3(1)+2y-3=4\\\\3+2y-3=4\\\\2y=4\\\\y=\frac{4}{2}\\\\y=2$