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", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"group": {"name": "group", "group": "Ungrouped variables", "definition": "repeat(random(-10..10 except 0),4)", "description": "", "templateType": "anything", "can_override": false}, "x1": {"name": "x1", "group": "Ungrouped variables", "definition": "group[0]", "description": "", "templateType": "anything", "can_override": false}, "y1": {"name": "y1", "group": "Ungrouped variables", "definition": "group[1]", "description": "", "templateType": "anything", "can_override": false}, "c1": {"name": "c1", "group": "Ungrouped variables", "definition": "x1*x+y1*y", "description": "", "templateType": "anything", "can_override": false}, "x2": {"name": "x2", "group": "Ungrouped variables", "definition": "group[2]", "description": "", "templateType": "anything", "can_override": false}, "y2": {"name": "y2", "group": "Ungrouped variables", "definition": "group[3]", "description": "", "templateType": "anything", "can_override": false}, "c2": {"name": "c2", "group": "Ungrouped variables", "definition": "x2*x+y2*y", "description": "", "templateType": "anything", "can_override": false}, "x": {"name": "x", "group": "Ungrouped variables", "definition": "random(-10..10)", "description": "", "templateType": "anything", "can_override": false}, "y": {"name": "y", "group": "Ungrouped variables", "definition": "random(-10..10)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "x1/x2<>y1/y2", "maxRuns": 100}, "ungrouped_variables": ["group", "x1", "y1", "c1", "x2", "y2", "c2", "x", "y"], "variable_groups": [], "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": "

Löse folgendes Gleichungssystem

\\begin{align}
\\simplify{ {x1}x + {y1}y} &=\\var{c1} \\\\
\\simplify{ {x2}x + {y2}y} &= \\var{c2}
\\end{align}

Gib die Werte für $x$ und $y$ ein:

$x = $ [[0]]

$y = $ [[1]]

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Löse folgendes Gleichungssystem

\\begin{align}
\\simplify{ {x1}x + {y1}y} &=\\var{c1} \\\\
\\simplify{ {x2}x + {y2}y} &= \\var{c2}
\\end{align}

Gib die Werte für $x$ und $y$ ein:

$x = $ [[0]]

$y = $ [[1]]

Löse folgendes Gleichungssystem

\\begin{align}
\\simplify{ {x1}x + {y1}y} &=\\var{c1} \\\\
\\simplify{ {x2}x + {y2}y} &= \\var{c2}
\\end{align}

Gib die Werte für $x$ und $y$ ein:

$x = $ [[0]]

$y = $ [[1]]

Löse folgendes Gleichungssystem

\\begin{align}
\\simplify{ {x1}x + {y1}y} &=\\var{c1} \\\\
\\simplify{ {x2}x + {y2}y} &= \\var{c2}
\\end{align}

Gib die Werte für $x$ und $y$ ein:

$x = $ [[0]]

$y = $ [[1]]

Löse folgendes Gleichungssystem

\\begin{align}
\\simplify{ {x1}x + {y1}y} &=\\var{c1} \\\\
\\simplify{ {x2}x + {y2}y} &= \\var{c2}
\\end{align}

Gib die Werte für $x$ und $y$ ein:

$x = $ [[0]]

$y = $ [[1]]

Löse folgendes Gleichungssystem

\\begin{align}
\\simplify{ {x1}x + {y1}y} &=\\var{c1} \\\\
\\simplify{ {x2}x + {y2}y} &= \\var{c2}
\\end{align}

Gib die Werte für $x$ und $y$ ein:

$x = $ [[0]]

$y = $ [[1]]

Löse folgendes Gleichungssystem

\\begin{align}
\\simplify{ {x1}x + {y1}y} &=\\var{c1} \\\\
\\simplify{ {x2}x + {y2}y} &= \\var{c2}
\\end{align}

Gib die Werte für $x$ und $y$ ein:

$x = $ [[0]]

$y = $ [[1]]

Löse folgendes Gleichungssystem

\\begin{align}
\\simplify{ {x1}x + {y1}y} &=\\var{c1} \\\\
\\simplify{ {x2}x + {y2}y} &= \\var{c2}
\\end{align}

Gib die Werte für $x$ und $y$ ein:

$x = $ [[0]]

$y = $ [[1]]

Löse folgendes Gleichungssystem

\\begin{align}
\\simplify{ {x1}x + {y1}y} &=\\var{c1} \\\\
\\simplify{ {x2}x + {y2}y} &= \\var{c2}
\\end{align}

Gib die Werte für $x$ und $y$ ein:

$x = $ [[0]]

$y = $ [[1]]

Löse folgendes Gleichungssystem

\\begin{align}
\\simplify{ {x1}x + {y1}y} &=\\var{c1} \\\\
\\simplify{ {x2}x + {y2}y} &= \\var{c2}
\\end{align}

Gib die Werte für $x$ und $y$ ein:

$x = $ [[0]]

$y = $ [[1]]

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