Higher June 2018 Paper 1 Q12

EdexcelHigherCurrent spec4 marksLinear Inequalities Simultaneous Equations

12 The diagram shows two straight lines drawn on a grid.

Grid with x from -2 to 10 and y from -2 to 10, showing the straight lines 3y = 2x + 6 and 4x + 3y = 24, which cross at (3, 4)

(a) Write down the solution of the simultaneous equations\[\begin{aligned}3y &= 2x + 6\\ 4x + 3y &= 24\end{aligned}\] (1)

(b) Show, by shading on the grid, the region defined by all five of the inequalities\[x \geqslant 0 \qquad y \geqslant 0 \qquad x + y \geqslant 4 \qquad 3y \leqslant 2x + 6 \qquad 4x + 3y \leqslant 24\]Label the region R. (3)

Graph from the end of the mark scheme: the lines 3y = 2x + 6, 4x + 3y = 24 and x + y = 4 drawn dashed; everything outside the wanted region is shaded, leaving unshaded the region R bounded by x + y = 4, 3y = 2x + 6, 4x + 3y = 24 and the x-axis, with vertices (1.2, 2.8), (3, 4), (6, 0) and (4, 0) — Mark scheme (b)

Scheme	Marks
\(x = 3\), \(y = 4\)	B1
	(1)

Scheme	Marks
Answer: Correct region (graph at end of mark scheme)	B3
	(3)
	(4 marks)

Notes