Practice
Graphing Systems of Inequalities Practice
Fifty original questions covering overlaps, regions, ordered pairs, quadrants, incompatible systems, and modeling.
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Question 1
Explanation
\((0,0)\) satisfies each configured constraint; every distractor fails at least one.
Question 2
Explanation
\((0,0)\) satisfies each configured constraint; every distractor fails at least one.
Question 3
Explanation
\((0,0)\) satisfies each configured constraint; every distractor fails at least one.
Question 4
Explanation
\((2,1)\) satisfies each configured constraint; every distractor fails at least one.
Question 5
Explanation
\((0,0)\) satisfies each configured constraint; every distractor fails at least one.
Question 6
Explanation
\((0,0)\) satisfies all boundaries and appears in the clipped intersection region.
Question 7
Explanation
\((0,0)\) satisfies all boundaries and appears in the clipped intersection region.
Question 8
Explanation
\((0,0)\) satisfies all boundaries and appears in the clipped intersection region.
Question 9
Explanation
\((2,1)\) satisfies all boundaries and appears in the clipped intersection region.
Question 10
Explanation
\((0,0)\) satisfies all boundaries and appears in the clipped intersection region.
Question 11
Explanation
The highlighted polygon is computed from points satisfying both constraints, so the labeled overlap is Region A.
Question 12
Explanation
The highlighted polygon is computed from points satisfying both constraints, so the labeled overlap is Region A.
Question 13
Explanation
The highlighted polygon is computed from points satisfying both constraints, so the labeled overlap is Region A.
Question 14
Explanation
The highlighted polygon is computed from points satisfying both constraints, so the labeled overlap is Region A.
Question 15
Explanation
The highlighted polygon is computed from points satisfying both constraints, so the labeled overlap is Region A.
Question 16
Explanation
Exactly \(0\) configured operators are strict, so that many boundaries are dashed.
Question 17
Explanation
Exactly \(1\) configured operator is strict, so that many boundaries are dashed.
Question 18
Explanation
Exactly \(0\) configured operators are strict, so that many boundaries are dashed.
Question 19
Explanation
Exactly \(2\) configured operators are strict, so that many boundaries are dashed.
Question 20
Explanation
Exactly \(0\) configured operators are strict, so that many boundaries are dashed.
Question 21
Explanation
The x- and y-sign constraints place every solution in Quadrant I.
Question 22
Explanation
The x- and y-sign constraints place every solution in Quadrant II.
Question 23
Explanation
The x- and y-sign constraints place every solution in Quadrant III.
Question 24
Explanation
The x- and y-sign constraints place every solution in Quadrant IV.
Question 25
Explanation
The x- and y-sign constraints place every solution in Quadrant IV.
Question 26
Explanation
A system uses logical AND. \((2,1)\) belongs to the intersection because every substituted statement is true.
Question 27
Explanation
A system uses logical AND. \((-3,2)\) belongs to the intersection because every substituted statement is true.
Question 28
Explanation
A system uses logical AND. \((3,-2)\) belongs to the intersection because every substituted statement is true.
Question 29
Explanation
A system uses logical AND. \((-3,2)\) belongs to the intersection because every substituted statement is true.
Question 30
Explanation
A system uses logical AND. \((4,0)\) belongs to the intersection because every substituted statement is true.
Question 31
Explanation
The renderer clips the coordinate window successively against every constraint, leaving exactly their intersection.
Question 32
Explanation
The renderer clips the coordinate window successively against every constraint, leaving exactly their intersection.
Question 33
Explanation
The renderer clips the coordinate window successively against every constraint, leaving exactly their intersection.
Question 34
Explanation
The renderer clips the coordinate window successively against every constraint, leaving exactly their intersection.
Question 35
Explanation
The renderer clips the coordinate window successively against every constraint, leaving exactly their intersection.
Question 36
Explanation
The system requires \(y>2\) and \(y<0\) simultaneously, which is impossible.
Question 37
Explanation
The system requires \(y>3\) and \(y<1\) simultaneously, which is impossible.
Question 38
Explanation
The system requires \(y>4\) and \(y<2\) simultaneously, which is impossible.
Question 39
Explanation
The system requires \(y>5\) and \(y<3\) simultaneously, which is impossible.
Question 40
Explanation
The system requires \(y>6\) and \(y<4\) simultaneously, which is impossible.
Question 41
Explanation
Each sentence supplies one half-plane, and both must hold. The correct system is \(x+y\le12\text{ and }x\ge3\).
Question 42
Explanation
Each sentence supplies one half-plane, and both must hold. The correct system is \(x+y\ge8\text{ and }y<6\).
Question 43
Explanation
Each sentence supplies one half-plane, and both must hold. The correct system is \(x+y\le90\text{ and }y\ge20\).
Question 44
Explanation
Each sentence supplies one half-plane, and both must hold. The correct system is \(x+y>30\text{ and }x<12\).
Question 45
Explanation
Each sentence supplies one half-plane, and both must hold. The correct system is \(x+y\ge50\text{ and }y\le2x\).
Question 46
Explanation
A system uses logical AND. Union shading includes points that fail another constraint, so only the common overlap is valid.
Question 47
Explanation
A system uses logical AND. Union shading includes points that fail another constraint, so only the common overlap is valid.
Question 48
Explanation
A system uses logical AND. Union shading includes points that fail another constraint, so only the common overlap is valid.
Question 49
Explanation
A system uses logical AND. Union shading includes points that fail another constraint, so only the common overlap is valid.
Question 50
Explanation
A system uses logical AND. Union shading includes points that fail another constraint, so only the common overlap is valid.
Keyboard: use Tab to move, arrow keys to change answer choices, and Enter to check an answer.
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Questions to review
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- Question 1Testing system solution pointsEasy
- Question 2Testing system solution pointsEasy
- Question 3Testing system solution pointsEasy
- Question 4Testing system solution pointsEasy
- Question 5Testing system solution pointsEasy
- Question 6Reading system overlapEasy
- Question 7Reading system overlapEasy
- Question 8Reading system overlapEasy
- Question 9Reading system overlapEasy
- Question 10Reading system overlapEasy
- Question 11Labeled-region identificationEasy
- Question 12Labeled-region identificationEasy
- Question 13Labeled-region identificationEasy
- Question 14Labeled-region identificationEasy
- Question 15Labeled-region identificationEasy
- Question 16Mixed boundary stylesMedium
- Question 17Mixed boundary stylesMedium
- Question 18Mixed boundary stylesMedium
- Question 19Mixed boundary stylesMedium
- Question 20Mixed boundary stylesMedium
- Question 21Quadrant analysisMedium
- Question 22Quadrant analysisMedium
- Question 23Quadrant analysisMedium
- Question 24Quadrant analysisMedium
- Question 25Quadrant analysisMedium
- Question 26Multiple-boundary reasoningMedium
- Question 27Multiple-boundary reasoningMedium
- Question 28Multiple-boundary reasoningMedium
- Question 29Multiple-boundary reasoningMedium
- Question 30Multiple-boundary reasoningMedium
- Question 31Meaning of the solution regionMedium
- Question 32Meaning of the solution regionMedium
- Question 33Meaning of the solution regionMedium
- Question 34Meaning of the solution regionMedium
- Question 35Meaning of the solution regionMedium
- Question 36Empty system intersectionsMedium
- Question 37Empty system intersectionsMedium
- Question 38Empty system intersectionsMedium
- Question 39Empty system intersectionsMedium
- Question 40Empty system intersectionsMedium
- Question 41Contextual systems of inequalitiesHard
- Question 42Contextual systems of inequalitiesHard
- Question 43Contextual systems of inequalitiesHard
- Question 44Contextual systems of inequalitiesHard
- Question 45Contextual systems of inequalitiesHard
- Question 46System graph error analysisHard
- Question 47System graph error analysisHard
- Question 48System graph error analysisHard
- Question 49System graph error analysisHard
- Question 50System graph error analysisHard