Can we find an integer solution to three simultaneous inequalities?

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From the inequalities \[y-2x>0,\qquad x+y>3,\qquad 2y-x<5\] deduce that \[\frac{1}{3}< x < \frac{5}{3},\qquad 2< y <\frac{10}{3},\] and hence that the given inequalities cannot be satisfied simultaneously by integral values of \(x\) and \(y\).

[The phrase ‘integral values’ means the same as ‘integer values’. ]