solve by elinination x-y-2z=4,-x+2y+z=1 and -x+y-3z=11

Question

I have to solve this equation by elmimination x-y-2z=4,-x+2y+z=1 and -x+y-3z=11.

Answer 1

Adds the first equation to the second equation:

 

(x-y-2z)+ (-x +2y+z) = 4+ 1

 y - z = 5 <--- please label this equation ALPHA; we will need it very soon!!!

 

Adds the first equation to the third equation:

 (x-y-2z) + (-x + y - 3z) = 4 + 11

 

 -5z = 15

   So z = -3

 

Plugging this into equation ALPHA above:

 y - z = 5

 y - (-3) = 5

 y + 3 = 5

 y +3 - 3 = 5 - 3

  y  = 2

 

Plugging these into the original second equation:

 

  -x + 2y + z = 1

  -x + 2(2) + -3 = 1

 -x + 4 + -3 = 1

 -x + 1 = 1

 -x + 1 + -1 = 1 + -1

  -x = 0

 x = 0

 

x=0. y = 2, z = -3

 

check:

   x - y - 2z = 0 - 2 - 2(-3) = 0 - 2 - (-6) = -2 - (-6) = -2 + 6 = 4

 

  -x + 2y + z = -0 + 2(2) + -3 = 0 + 4 + -3 = 4 + -3 = 1

 

  -x + y - 3z = -0 + 2 - 3(-3) = 0 + 2 - (-9) = 2 - (-9) = 2 + 9 = 11

 

x=0. y = 2, z = -3