Question

Solve the systems of linear inequations graphically.

(i) x + y ≥ 1, 7x + 9y ≤ 63, x ≤ 6, y ≤ 5, x ≥ 0, y ≥ 0

(ii) 2x + 3y ≤ 35, y ≥ 3, x ≥ 2, x ≥ 0, y ≥ 0

Answer 1

(i) x + y ≥ 1, 7x + 9y ≤ 63, x ≤ 6, y ≤ 5, x ≥ 0, y ≥ 0

First, we shall plot the graph of the equation and shade the side containing solutions of the inequality,

Now, we can choose any value but find the two mandatory values which are at x = 0 and y = 0, i.e., x and y–intercepts always,

x + y ≥ 1

Therefore when,

x	0	2	1
y	1	-1	0

7x + 9y ≤ 63

Therefore when,

x	0	5	9
y	7	3.11	0

x ≤ 6, y ≤ 5 and x ≥ 0, y ≥ 0

(ii) 2x + 3y ≤ 35, y ≥ 3, x ≥ 2, x ≥ 0, y ≥ 0

Firstly, we shall plot the graph of the equation and shade the side containing solutions of the inequality,

Now, we can choose any value but find the two mandatory values which are at x = 0 and y = 0, i.e., x and y–intercepts always,

2x + 3y ≤ 35

Therefore when,

x	0	5	17.5
y	11.667	8.33	0

y ≥ 3, x ≥ 2, x ≥ 0, y ≥ 0