Question

Please help me with this linear inequalities as graphs question!

Answer 1

The system of linear inequalities which satisfy the region R in the graph above are:

1. y ≤ 2x + 3
2. y ≥ -x + 4
3. y ≤ x + 4

How to find the inequalities?

Mathematically, the general equation of a straight line is given by y = mx + b.

In order to determine the system of linear inequalities that satisfy the region R, we would identify the points through which these straight lines passes through.

For the left line, we have:

y-intercept = 3.

x-intercept = -3/2.

Points (x, y) = (0, 3) and (-3/2, 0).

Thus, the inequality is given by:

(x/-3/2) + y/3 ≤ 1.

-2x + y ≤ 3

y ≤ 2x + 3

For the right line, we have:

y-intercept = 4.

x-intercept = 4.

Points (x, y) = (0, 4) and (4, 0).

Thus, the inequality is given by y ≥ -x + 4

For the lower line, we have:

y-intercept = 0.

x-intercept = 4.

Points (x, y) = (4, 0)

Thus, the inequality is given by y ≤ x + 4

In conclusion, the system of linear inequalities which satisfy the region R in the graph above are:

• y ≤ 2x + 3

• y ≥ -x + 4

• y ≤ x + 4

Read more on linear inequalities here: brainly.com/question/21103162

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