SOLUTION: find the solution set for the system of equations x-y+z=2 x+y+3z=6 3x-y+5z=10

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Question 386509: find the solution set for the system of equations
x-y+z=2
x+y+3z=6
3x-y+5z=10
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The determinant of the system is zero.
There are an infinite number of solutions.
One of the equations is a linear combination of the other two.
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1.x-y%2Bz=2
2.x%2By%2B3z=6
3.3x-y%2B5z=10
From eq. 1 and eq. 2,
x-y%2Bz%2Bx%2By%2B3z=2%2B6
2x%2B4z=8
4.x%2B2z=4
From eq. 1 and eq. 3,
x%2By%2B3z%2B3x-y%2B5z=6%2B10
4x%2B8z=16
5.x%2B2z=4
So then x%2B2z=4
x=4-2z
Plug that into eq. 1,
4-2z-y%2Bz=2
y%2Bz=2
y=2-z
So the solution set is (4-2z,2-z,z)