(a) On the graph paper below, draw the region which satisfies all of the following inequalities.\[\begin{array}{l} x + y \leqslant 6 \\[4pt] y \geqslant \dfrac{x}{2} + 3 \\[4pt] x \geqslant -2. \end{array}\]
Clearly indicate the region that represents your answer. [3]
(b)
(i) What is the greatest possible value of \(x\) such that all three conditions are met? [1]
\(x =\) ………………………
(ii) What is the greatest possible value of \(y\) such that all three conditions are met? [1]
\(y =\) ………………………
Mark scheme (a)
Scheme
Marks
Comments
Any two of the three lines correct. (x + y = 6 y = x/2 + 3 x = −2)
B2
B1 for any one line correct.
Correct region identified.
B1
CAO.
Mark scheme (b)
Scheme
Marks
Comments
(i) (x =) 2
B1
FT ‘their region’, if possible, for both B1 marks, provided it is of equivalent difficulty.
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