- #1
Brutus
- 7
- 0
Homework Statement
Solve:
[tex]
\left\{ \begin{array}
{ccc} 5x - y - z & = & 4 \\
x - y + 2z & = & -5
\end{array} \right.
[/tex]
If the system has infinite solution, does it fill the entire space?
The Attempt at a Solution
I know the system is underdetermined since the number of variables is less than the number of given equations, so my first step was to find out whether this system is consistent(has at least one solution).
[tex]
5x - y - 4 & = & \frac{-x}{2} + \frac{y}{2} - \frac{5}{2} \\
y & = & \frac{11x}{3} - 1
[/tex]
The system is consistent and has infinite solution.
Now, the real question, is the solution constrained to a plane or does it fill the entire space?
How do you find out? I've thought about it, and I am completely lost.
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