2y+z=-8 and x-2y-3z=0 and -x+y+2z=3

Question

this is my hw and i really need help!

Answer 1

Elimination method

Given equations are 2y+z = -8 ---> (1)

x-2y-3z = 0 ---> (2)

-x+y+2z = 3 ---> (3)

Multiple to each side by 2.

-2x+2y+4z = 6 ---> (4)

To eliminate the y value add  (1)&(2).

   2y+z = -8

x-2y-3z = 0

____________________

x-2z = -8 ---> (5)

To eliminate the y value add (2)&(4).

   x-2y-3z = 0

-2x+2y+4z = 6

______________

-x+z = 6 ---> (6)

To eliminate the x value add the equations (5)&(6).

x-2z = -8

-x+z = 6

_____________

-z = -2

Cancell the same signs.

z = 2

Substitute the z value in (1).

2y+2 = -8

Subtract 2 from each side.

2y = -10

Divide to each side by 2.

y = -5.

Substitute the z,y value in (2).

x+10-6 = 0

x+4 = 0

Subtract 4 from side.

x = -4

Solution x = -4, y = -5, z = 2.