Karen Morrison and Nick Hamshaw Solutions for Exercise 6: Exercise 14.6

By shading the unwanted regions, show the region defined by the set of inequalities $x+2y⩾6$, $y⩽x$ and $x<4$

By shading the unwanted regions, show the region defined by the set of inequalities $x+y⩾5$, $y⩽2$ and $y⩾0$

On a grid, draw the lines $x=4$, $y=3$ and $x+y=5$

By shading the unwanted regions, show the region that satisfies all the inequalities $x⩽4$, $y⩽3$ and $x+y⩾5$. Label the region R.

Write down the three inequalities that define the unshaded triangular region R.

The unshaded region in diagram represents the set of inequalities $y⩾0$, $y+2x⩾2$ and $x+y<4$. Write down the pair of integers $\left(x,y\right)$ that satisfies all the inequalities.

Draw graph to show the solution sets of the inequalities: $y⩽4$, $y⩾x+2$ and $3x+y⩾4$. Write down the integer co-ordinates$\left(x,y\right)$ that satisfies all the inequalities in this case.