Question

Diagram 8 shows a system of linear inequalities in two variables drawn on a Cartesian plane. Given

that variable x is the number of shirts while variable y is the number of pants in a wardrobe.
y=-x+6
Diagram 8
(i)
State three linear inequalities that define the shaded region in Diagram 8 above.
(ii)
Determine the maximum number of shirts if there are 5 pants in the wardrobe.
[4 marks]

Answer 1

The three linear inequalities that define the shaded region in Diagram 8 are

y ≥ -x + 6

y > -x

y ≤ 6

The maximum number of shirts, if there are 5 pants in the wardrobe. is 4

How to find maximum number of shirts

We examine the diagram 8, to observe that the points in the shaded area are within the solution. Also, points on the boundary with solid line are part of the solution

When the number of pants is 5, we trace from t = 5 to the graph. This intersects the line at a point where x is equal to1. And continues to x = 5.

Since x = 5 is on a dashed line which is not part of the solution we go to the nearest point, in the shaded area. This point is 4

We can therefore say =, the