SOLUTION: Solve x + y + z = 5 x - 2y + z = 8 3x - y

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Question 65845This question is from textbook An Incremental Development
: Solve
x + y + z = 5
x - 2y + z = 8
3x - y - z = 3 This question is from textbook An Incremental Development

Found 2 solutions by ptaylor, ankor@dixie-net.com:
Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
Solve
(1) x + y + z = 5
(2) x - 2y + z = 8
(3) 3x - y - z = 3
Lets add eq (1) & (3) and we get:
4x=8
x=2
Substitute x=2 in Eq (1) & (2) and we have:
(1) 2 + y + z = 5
(2) 2 - 2y + z = 8
subtract (2) from (1) getting:
3y=-3
y=-1
Substitute x=2 and y=-1 in (1) and we have:
(1) 2 + (-1) + z = 5
1+z=5 subtract 1 from both sides:
z=4

Ck by substituting x=2, y=-1 and z=4 in the original eqs.

Hope this helps---ptaylor

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
x + y + z = 5
x - 2y + z = 8
3x - y - z = 3
:
The problem lends itself the elimination method
Add the 1st and 3rd equations and find x:
x + y + z = 5
3x - y - z = 3
------------------add
4x + 0y + 0z = 8
x = 8/4
x = 2
:
Substitute 2 for x in the 2nd and 3rd equations
2 - 2y + z = 8
3(2) -y - z = 3
:
2 - 2y + z = 8
6 - y - z = 3
--------------- add
8 - 3y + 0z = 11
-3y = 11 - 8
y = 3/-3
y = -1
:
I'll let you find the value of z. Check solutions in the original equations.

SOLUTION: Solve x + y + z = 5 x - 2y + z = 8 3x - y - z = 3