SOLUTION: Hi I am a student studying algebra 2 I do not seem to get how to solve x+y+2z= 11 and x+y+3z=14 and x+2y-z=5 because I am not able to figure out how we get x y and z...

 

Hi,

x+y+2z= 11 and 

x+y+3z=14 

x+y+2z= 11 and

-x-y-3z=-14   |Subtract 2nd from first to eliminate x & y

      -z = -3

     

x+y+3z=14 and 

x+2y-z=5

x+y+9=14 and    |Substitute z = 3

x+2y-3=5

x+y = 5 and 

x+2y = 8

x+y = 5 and 

-x-2y = -8    |Subtract 2nd from first to eliminate x

      -y = -3

        and x+y+2z= 11 ⇒ x + 3 + 6 = 11  

(2, 3, 3) the solution for this system