线性方程组基础范例

几何画板及绘图内容加载中，请稍等……

2021-06-13 20:39

所属专题 A Plethora of Practice Problems

①本范例演示了线性方程组的图形解法，通过几何图形直观展示方程组的交点；②涉及的核心数学概念包括线性方程、几何图形交点、解析几何；③作图要点提炼自构造摘要，使用了RandomElement, If, RandomDiscrete, Textfield, FractionText等GeoGebra命令与对象，如List1, A_{s2}, B_{s2}等；④适合高中数学教学，用于帮助学生理解线性方程组的解及其几何意义。

GeoGebra 命令及参数

RandomElement(List1a) → D_{s2}
If(B_{s2} / D_{s2} ≟ A_{s2}, (-D_{s2}), D_{s2}) → D_{s}
RandomElement(List1a) → C_{s1}
RandomElement(List1a) → B_{s1}
RandomElement(List1a) → A_{s1}
If(A_{s1} / C_{s1} ≟ B_{s1}, (-C_{s1}), C_{s1}) → C_{s}
RandomDiscrete({1, 2, 3, 4, 5, 6, 7}, {10, 4, 3, 2, 1, 0, 2}) → a
RandomDiscrete({1, 2, 3, 4, 5, 6, 7}, {10, 3, 3, 2, 1, 0, 2}) → b_{1}
If(b_{1} ≟ 7 ∧ a ≟ 7, 1, b_{1}) → b
If(a ≟ 1, RandomElement[List1], a ≟ 6, RandomElement[List6], RandomElement[List7], a ≟ 2, RandomElement[List2], a ≟ 3, RandomElement[List3], a ≟ 4, RandomElement[List4], a ≟ 5, RandomElement[List5]) → m_{e}
If(b ≟ 1, RandomElement[List1], b ≟ 6, RandomElement[List6], RandomElement[List7], b ≟ 2, RandomElement[List2], b ≟ 3, RandomElement[List3], b ≟ 4, RandomElement[List4], b ≟ 5, RandomElement[List5]) → n_{e}
If(a ≟ 1, RandomElement[List1a], a ≟ 6, RandomElement[List6a], RandomElement[List7a], a ≟ 2, RandomElement[List2a], a ≟ 3, RandomElement[List3a], a ≟ 4, RandomElement[List4a], a ≟ 5, RandomElement[List5a]) → A_{e}
If(a ≟ 1, RandomElement[List1a], a ≟ 6, RandomElement[List6a], RandomElement[List7a], a ≟ 2, RandomElement[List2a], a ≟ 3, RandomElement[List3a], a ≟ 4, RandomElement[List4a], a ≟ 5, RandomElement[List5a]) → C_{e}
If(b ≟ 1, RandomElement[List1a], b ≟ 6, RandomElement[List6a], RandomElement[List7a], b ≟ 2, RandomElement[List2a], b ≟ 3, RandomElement[List3a], b ≟ 4, RandomElement[List4a], b ≟ 5, RandomElement[List5a]) → B_{e}
If(b ≟ 1, RandomElement[List1a], b ≟ 6, RandomElement[List6a], RandomElement[List7a], b ≟ 2, RandomElement[List2a], b ≟ 3, RandomElement[List3a], b ≟ 4, RandomElement[List4a], b ≟ 5, RandomElement[List5a]) → D_{1}
If(A_{e} / C_{e} ≟ B_{e} / D_{1}, (-D_{1}), D_{1}) → D_{e}
RandomDiscrete({1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10, -10, 0}, {8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6}) → m_{s}
RandomDiscrete({1, -1, 2, -2, 3, -3, 4, -4, 5, -5, 6, -6, 7, -7, 8, -8, 9, -9, 10, -10, 0}, {8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6}) → n_{s}
RandomElement({2, 3, 4, 5, 6, -2, -3, -4, -5, -6}) → howmuchbigger
If(Choice ≟ 1, ((-C_{s}) * howmuchbigger), Choice ≟ 2, (C_{s} * howmuchbigger), Choice ≟ 3, howmuchbigger, Choice ≟ 4, howmuchbigger, Choice ≟ 5, (A_{e} * howmuchbigger)) → A_{big}
If(Choice ≟ 1, howmuchbigger, Choice ≟ 2, howmuchbigger, Choice ≟ 3, ((-D_{s}) * howmuchbigger), Choice ≟ 4, (D_{s} * howmuchbigger), Choice ≟ 5, (B_{e} * howmuchbigger)) → B_{big}
If(Choice ≟ 1, (D_{s1} * howmuchbigger) + RandomElement[List1], Choice ≟ 2, (D_{s1} * howmuchbigger) + RandomElement[List1], Choice ≟ 3, (C_{s2} * howmuchbigger) + RandomElement[List1], Choice ≟ 4, (C_{s2} * howmuchbigger) + RandomElement[List1], Choice ≟ 5, (R_{e} * howmuchbigger) + RandomElement[List1]) → nosolution
If(Choice ≟ 1, (D_{s1} * howmuchbigger), Choice ≟ 2, (D_{s1} * howmuchbigger), Choice ≟ 3, (C_{s2} * howmuchbigger), Choice ≟ 4, (C_{s2} * howmuchbigger), Choice ≟ 5, (R_{e} * howmuchbigger)) → infsolutions
If(Choice ≟ 1, m_{s}, Choice ≟ 2, m_{s}, Choice ≟ 3, m_{s}, Choice ≟ 4, m_{s}, Choice ≟ 5, m_{e}) → x_{ans1}
If(Choice ≟ 1, n_{s}, Choice ≟ 2, n_{s}, Choice ≟ 3, n_{s}, Choice ≟ 4, n_{s}, Choice ≟ 5, n_{e}) → y_{ans1}
If(answercode ≟ 1, x_{ans1}, answercode ≟ 2, -1000, answercode ≟ 3, 1000) → x_{ans}
If(answercode ≟ 1, y_{ans1}, answercode ≟ 2, -1000, answercode ≟ 3, 1000) → y_{ans}
Textfield(x_{guess}) → InputBox1
Textfield(y_{guess}) → InputBox2
FractionText((x_{ans}, y_{ans})) → fractext

AI 绘图提示语参考

请绘制一个包含两条直线的图形，两条直线相交于一点，并标注交点坐标。图形中应包含代表直线的线段，以及一个明显的交点标记。交点附近可添加文本标签显示坐标值。整体构图应清晰简洁，便于理解线性方程组的几何解法。

以上提示语为根据原始绘图命令整理而来，仅供参考。