Review question

# Can we find an integer solution to three simultaneous inequalities? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5281

## Suggestion

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?