Solution:
(i) x – 2y ≥ 0, 2x – y ≤ –2, x ≥ 0, y ≥ 0
We’ll draw the equation’s graph and shade the side that has the inequality’s solutions.
You can choose any value, but you must always locate the two necessary values at x = 0 and y = 0, i.e., the x and y-intercepts.
x – 2y ≥ 0
So when,
| x | 0 | 2 | 4 |
| y | 0 | 1 | 2 |
2x – y ≤ –2
So when,
| x | 0 | 1 | -1 |
| y | 2 | 4 | 0 |
x ≥ 0, y ≥ 0
As we can see that, the lines never intersect each other for x ≥ 0, y ≥ 0, Therefore, we can conclude that there is no solution for the given inequations.
(ii) x + 2y ≤ 3, 3x + 4y ≥ 12, y ≥ 1, x ≥ 0, y ≥ 0
We’ll draw the equation’s graph and shade the side that has the inequality’s solutions.
You can choose any value, but you must always locate the two necessary values at x = 0 and y = 0, i.e., the x and y-intercepts.
x + 2y ≤ 3
So when,
| x | 0 | 1 | 3 |
| y | 1.5 | 1 | 0 |
3x + 4y ≥ 12
So when,
| x | 0 | 2 | 4 |
| y | 3 | 1.5 | 0 |
y ≥ 1, x ≥ 0, y ≥ 0
