Question 270365: A student says that the system consisting of x=0, y=0, and z=0 has no solutions. Explain the student's error. Write and solve a system.
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Of course the system has a solution, namely the ordered triple (0, 0, 0)
Nothing to write. The system is already written, namely:
x=0, y=0, and z=0
These are the equations of the three coordinate axes in 
John
Answer by Edwin McCravy(20060)  (Show Source):
You can put this solution on YOUR website!
The student's error is that 0 is a number,
and therefore is a perfectly good answer.
This system
We can eliminate y by adding the first two equations
just as they are:
x + y + z = 0
x - y + z = 0
-------------
2x +2z = 0
We can eliminate y and z by adding the last two equations:
x - y + z = 0
x + y - z = 0
-------------
2x = 0
So we have the system:
Solve the second one for s,
2x = 0
x = 0
Substitute in
2x + 2z = 0
2(0) + 2z = 0
2z = 0
z = 0
Substitute in one of the original equations:
x + y + z = 0
0 + y + 0 = 0
y = 0
Edwin
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