When do these simultaneous equations have a positive solution?

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There are positive real numbers \(x\) and \(y\) which solve the equations \[2x + ky = 4, \qquad x+y = k\] for

1. all values of \(k\);

2. no values of \(k\);

3. \(k=2\) only;

4. only \(k>-2\).