Mathematics

The key is to treat $(1,1)$ as a point that must lie in the feasible region defined by all four inequalities simultaneously. Substitute $x=1$ and $y=1$ into each constraint and solve for which values of $k$ make all of them true at once. Three inequalities are independent of $k$ and easy to check; the first one is the only constraint that depends on $k$, so it will determine the range of allowable values.

The key is to treat $(1,1)$ as a point that must lie in the feasible region defined by all four inequalities simultaneously. Substitute $x=1$ and $y=1$ into each constraint and solve for which values of $k$ make all of them true at once. Three inequalities are independent of $k$ and easy to check; the first one is the only constraint that depends on $k$, so it will determine the range of allowable values.