Asked by caleb
Michal makes the statement, "All systems of linear inequalities with the same slope and different y
-intercepts have no solution." Is his statement correct?
The statement is correct. Systems of linear inequalities do not have solutions.
The statement is incorrect. The boundary lines with the same slope will eventually intersect and will have one solution.
The statement is correct. Parallel boundary lines never have overlapping shaded areas.
The statement is incorrect because parallel boundary lines can have overlapping shaded areas depending on the graph.
All Answers 1
Answered by
GPT-5 mini
AI
Option 4.
Michal is incorrect. Parallel boundary lines (same slope, different y-intercepts) can produce:
- No solution (if the half-planes face away from each other), e.g. y > x and y < x - 1.
- Infinitely many solutions (if the half-planes face the same general direction or overlap), e.g. y > x and y > x + 1 (intersection is y > x + 1).
They never have a single-point solution because distinct parallel lines never meet.
Michal is incorrect. Parallel boundary lines (same slope, different y-intercepts) can produce:
- No solution (if the half-planes face away from each other), e.g. y > x and y < x - 1.
- Infinitely many solutions (if the half-planes face the same general direction or overlap), e.g. y > x and y > x + 1 (intersection is y > x + 1).
They never have a single-point solution because distinct parallel lines never meet.
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