From the inequalities \[y-2x>0,\qquad x+y>3,\qquad 2y-x<5\] deduce that \[\frac{1}{3}< x < \frac{5}{3},\qquad 2< y <\frac{10}{3},\]

Where do the three lines \[\begin{align*} y-2x &= 0 \\ x+y &=3 \\ 2y-x &=5 \end{align*}\]

lie in the plane?

On which side of each of these lines does the respective inequality hold?

… and hence that the given inequalities cannot be satisfied simultaneously by integral values of \(x\) and \(y\).

Which integer values of \(x\) and \(y\) do we need to consider?