x+y+z=0, x-y+2z=5, 3x+y+z=8 now solve for x,y,and z

Question

solving the system using x,y,and z .find the value of each

Answer 1

x+y+z=0, x-y+2z=5, 3x+y+z=8 now solve for x,y,and z

 3x + y + z = 8
-(x + y + z = 0)
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 2x            = 8
x = 4

x + y + z = 0           x - y + 2z = 5
4 + y + z = 0          4 - y + 2z = 5
      y + z = -4            - y + 2z = 1

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

x + y + z = 0
4 + y + -1 = 0
y = 0 - 4 + 1
y = -3

Always check the answers.

3x + y + z = 8
3(4) + (-3) + (-1) = 8
12 - 3 -1 = 8
8 = 8

x - y + 2z = 5
4 - (-3) + 2(-1) = 5
4 + 3 - 2 = 5
5 = 5

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