Question

09. Escalone, se necessário, e resolva os sistemas:

Answer 1

a) x+y+z=4
      3y +z=8
          -3z=3    z=-3/3   z=-1

3y+z=8       3y=8-z   3y =8- (-1)     3y=8+1    3y=9    y=9/3    y=3

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

b) x+y+z=1
    x-y+3z=9
   4x-y-z=4

x+y+z=1     z=1-x-y

x-y+3(1-x-y)=9
x-y+3-3x-3y=9
-2x-4y=6  (-1)       2x+4y=-6   2x=-6-4y     x=(-6-4y)/2

4x-y-z=4
4(-6-4y)/2 - y -(1-x-y)=4
2(-6-4y)-y-1+x+y=4
-12-8y-y-1+x+y=4
x-8y-13=4
x=8y+17


z=1-x-y      z=1-(8y+17)-y   z=1-8y-17-y   z=-9y-16

x-y+3z=9          x+3z-9=y         

8y+17+3(-9y-16)-9=y    8y+17-27y-48-9=y    8y-27y-y=40

-20y=40   -y=2    y=-2


x=8y+17     x=8(-2)+17    x=1


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