Plot out (graph) the regions undefined by each of the following : 1. y \leqslant 5,x - y \leqslant 1 \\ ,4x + 3y \geqslant 12 2. x \geqslant 0,y \geqslant 0 \\ ,x + y < 6,y -…

Question

Plot out (graph) the regions undefined by each of the following :

1.

`y \leqslant 5,x - y \leqslant 1 \\ ,4x + 3y \geqslant 12`
2.

`x \geqslant 0,y \geqslant 0 \\ ,x + y < 6,y - x < 2`
​

Answer 1

• See the attached

Explanation:

Q1

• y ≤ 5
• x - y ≤ 1 ⇒ y ≥ x - 1 (region A in the graph)
• 4x + 3y ≥ 12 ⇒ y ≥ - 4/3x + 4 (region B in the graph)

Regions covered by each functions are shaded and the intersection also shaded and marked.

The white area in the graphs is the undefined region.

Q2

• x ≥ 0, y ≥ 0 - these limit the region to the first quadrant
• x + y < 6 ⇒ y < -x + 6 (region A in the graph))
• y - x < 2 ⇒ y < x + 2 (region B in the graph)

Regions covered by each functions are shaded and the intersection also shaded and marked.

The white area in the graph is the undefined region.