// Numbas version: exam_results_page_options
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{"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "part a", "variables": ["a1", "b1", "a2", "b2", "a3", "b3", "c11", "c12", "c1", "c2", "c3", "c21", "c22", "c31", "c32", "xf1", "f1"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>P-{a1+1}{a2-1}{a3+2}{b1+2}{b2-2}{b3+1}: Is the following constraint satisfiable?</p>\n<p>$(\\simplify{{c11} X + {c12} Y = {c1}})$ $\\land$ $(\\simplify{{c21} X + {c22} Y = {c2}})$ $\\land$ $(\\simplify{{c31} X + {c32} Y} \\leq \\var{c3})$</p>\n<p><strong>Step 1: </strong>Isolate $Y$ in the first primitive:</p>\n<p>$Y$ = [[0]]</p>\n<p><strong>Step 2: </strong>Propagate:</p>\n<p>$(Y=$[[0]]$) \\land ($[[1]]$=&nbsp; \\var{c2}) \\land ($[[2]]$\\leq \\var{c3})$</p>\n<p></p>\n<p><strong>Step 3-</strong><strong>Conclusion:</strong> We find that given constraint is satisfied for any number</p>\n<p>$X$[[5]][[3]]</p>\n<p>and $Y$ = [[4]]</p>\n<p></p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": "1", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{-c11/c12}*X+{c1/c12}", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, 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