// Numbas version: exam_results_page_options
{"name": "Simultaneous Equations with integers as solutions.", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "x", "y", "f", "g"], "name": "Simultaneous Equations with integers as solutions.", "tags": ["integer solutions", "linear equations", "simultanenous equations", "solving equations", "solving linear equations"], "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>Solve the simultaneous equations:</p>\n<p style=\"text-align: center;\">$\\simplify[all,!noLeadingMinus]{{a}x+{b}y = {f}}$</p>\n<p style=\"text-align: center;\">$\\simplify[all,!noLeadingMinus]{{c}x+{d}y = {g}}$</p>\n<p style=\"text-align: left;\">$x=\\;$[[0]]</p>\n<p style=\"text-align: left;\">$y=\\;$[[1]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{x}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{y}", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>This question is set up by working \"backwards\" i.e. given the integer solutions for $x$ and $y$ and their coefficients gives the right-hand side of the equations.</p>\n<p>I have also insisted that the the coefficients in &nbsp;both equations are coprime and that, in order not to get degenerate equations, the determinant of the coefficients is non 0. Look at Testing in Variables to see this.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": "gcd(a,b)=1 and gcd(c,d)=1 and det(matrix([a,b],[c,d]))<>0"}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(-10..10 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(-10..10 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(-10..10 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(-10..10 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "c*x+d*y", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "a*x+b*y", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "y": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "y", "description": ""}, "x": {"definition": "random(-5..5 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "x", "description": ""}}, "metadata": {"notes": "", "description": "<p>A simultaneous equations question with integers only</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}]}], "contributors": [{"name": "steve kilgallon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/268/"}]}