(a) Given that \(x\) and \(y\) are integers such that \[\begin{gathered} 3 \lt x \lt 7 \\ 4 \lt y \lt 9 \\ \text{and } x + y = 13 \end{gathered}\] find all the possible values of \(x\). (2)
(b) On the grid below show, by shading, the region defined by the inequalities \(y \geqslant -1\) \(y \leqslant 4 - x\) \(y \leqslant 3x - 1\) Mark this region with the letter R.(4)
Mark scheme (a)
Answer
Mark
Notes
5 and 6
2
M1 for evidence that \((x =)\) 4, 5, 6 or evidence that \((y =)\) 5, 6, 7, 8 A1 cao
Mark scheme (b)
Answer
Mark
Notes
Region identified
4
M1 for two of the lines \(y = -1\), \(y = 3x - 1\) and \(y = 4 - x\) drawn M1 for three of the lines \(y = -1\), \(y = 3x - 1\) and \(y = 4 - x\) drawn M1 any correct shading (in or out) satisfying at least two of the inequalities where the shading must extend from the appropriate line A1 Fully correct region shown by either shading in, shading out or the use of R Accept lines that are solid or dashed
