The system of linear inequalities which satisfy the region R are:
- y < x - 3.
- y ≤ -2x + 5.
- y ≥ x.
How to find the inequalities?
Mathematically, the standard 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 the lines passes through.
For the broken line, we have:
y-intercept = 3.
x-intercept = -3.
Points (x, y) = (0, 3) and (-3, 0).
Since the line is broken (not equal to), the inequality is given by:
y < x - 3.
For the other line, we have:
y-intercept = 5.
x-intercept = -5/2.
Points (x, y) = (0, 5) and (-5/2, 0).
(x/-5/2) + y/5 ≤ 1
-2x + y ≤ 5
y ≤ -2x + 5
For the line passing through the origin, we have:
y - x ≥ 0
y ≥ x.
In conclusion, the system of linear inequalities which satisfy the region R are:
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