Question

Using the following equation , solve the equation graphically for integral values of x any.

Plot a graph of the equations and shade out the area which is not in the range of values.

1.

`y \geqslant 0 , \\ x - y \geqslant 1 , 3x + 4y < 12`
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Answer 1

{(1, 0), (2, 0), (2, 1)}

Explanation:

In the attached graph, the dashed lines are to be considered part of the unshaded area, hence in the solution set. The only points with integer coordinates in the solution set are the ones listed above.

Answer 2

• See the attached

Explanation:

• y ≥ 0 - limits the region to first and second quadrants
• x - y ≥ 1 ⇒ y ≤ x - 1 (region A on the graph)
• 3x + 4y < 12 ⇒ y < - 4/3x + 4 (region B on the graph)

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

The white area in the graph is the out of range region.