The graph of the inequalities ax+by sc, ax+by zc are
Correct answer: B. closed half planes
- A. open half planes
- B. closed half planes
- C. open and closed half planes
- D. None
Explanation
The graph of the inequalities \(ax + by \leq c\) and \(ax + by \geq c\) represent closed half planes. When the inequality is of the form \(ax + by \leq c\), it represents a closed half plane including the boundary line (the line represented by \(ax + by = c\)). Similarly, when the inequality is of the form \(ax + by \geq c\), it also represents a closed half plane including the boundary line.
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Linear equations contain variables only to the first power and produce straight-line relationships when represented graphically. Problems involve solving equations with brackets, fractions, and variables on both sides, forming equations from statements, and handling simultaneous linear equations, which differ from quadratic equations by having no squared variable.
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