8.4.1 ᠭᠤᠷᠪᠠᠨ ᠥᠯᠥ ᠮᠡᠳᠡᠭᠳᠡᠭᠴᠢᠳᠡᠢ ᠨᠢᠭᠡᠳᠤᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠤᠨ ᠪᠥᠯᠥᠭ
8.4 ᠭᠤᠷᠪᠠᠨ ᠥᠯᠥ ᠮᠡᠳᠡᠭᠳᠡᠭᠴᠢᠳᠡᠢ ᠨᠢᠭᠡᠳᠤᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠦᠨ ᠪᠥᠯᠥᠭ ᠦᠨ ᠪᠣᠳᠣᠬᠤ ᠠᠷᠭᠠ,ᠰᠤᠷᠬᠤ ᠬᠠᠷᠠᠯᠳ᠋ᠠ ᠄,1.ᠭᠤᠷᠪᠠᠨ ᠦᠯᠦ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠦᠬᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠤᠨ ᠪᠦᠯᠦᠭ᠌ ᠤᠨ ᠤᠬᠠᠠᠠᠳ᠋ᠠᠬᠤᠨ ᠢ ᠤᠢᠯᠠᠭᠠᠵᠤ ᠮᠡᠳ᠋ᠡᠭᠦ ᠃ 2. ᠬᠢᠯᠪᠠᠷ ᠭᠤᠷᠪᠠᠨ ᠦᠯᠦ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠦᠬᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠤᠨ ᠪᠦᠯᠦᠭ᠌ ᠢ ᠪᠤᠳ᠋ᠤᠵᠤ ᠴᠢᠳ᠋ᠠᠬᠤ ᠃,,ᠦᠯᠦ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢ ᠵᠢ ᠨᠢ ᠤᠰᠠᠳᠬᠠᠬᠤ,1. ᠬᠤᠶᠠᠷ ᠦᠯᠦ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠦᠬᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠦᠨ ᠪᠦᠯᠦᠭ᠌ ᠦᠨ ᠤᠬᠠᠭᠳᠠᠬᠤᠨ︖,2. ᠬᠤᠶᠠᠷ ᠦᠯᠦ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠦᠬᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠦᠨ ᠪᠦᠯᠦᠭ᠌ ᠢ ᠪᠣᠳᠣᠬᠤ ᠠᠷᠭᠠ ︖,ᠤᠷᠤᠯᠭᠤᠯᠬᠤ ᠠᠷᠭᠠ ᠪᠠ ᠨᠡᠮᠡᠵᠦ ᠬᠠᠰᠤᠬᠤ ᠠᠷᠭᠠ,ᠨᠢᠬᠡ ᠦᠯᠦ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠦᠬᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠪᠤᠯᠭᠠᠬᠤ,ᠰᠠᠭᠤᠷᠢ ᠮᠡᠳᠡᠯᠭᠡ ᠶᠢᠨ ᠡᠷᠬᠢᠴᠡᠭᠦᠯᠥᠯ,ᠬᠡᠷᠡᠯᠳ᠋ᠦ ᠳ᠋ᠦ 1 ᠲᠥᠭᠥᠷᠢᠭ᠂ 2 ᠲᠥᠭᠥᠷᠢᠭ᠂ 5 ᠲᠥᠭᠥᠷᠢᠭ ᠤᠨ ᠵᠤᠭᠤᠰ ᠨᠡᠢᠳ᠋ᠡ 12 ᠪᠤᠢ ᠂ ᠨᠡᠢᠳ᠋ᠡ 22 ᠲᠥᠭᠥᠷᠢᠭ ᠃ ᠡᠭᠦᠨ ᠳ᠋ᠦ 1 ᠲᠥᠭᠥᠷᠢᠭ᠌ ᠤᠨ ᠬᠠᠭᠤᠳ᠋ᠠᠰᠤᠨ ᠲᠤᠭᠠ ᠨᠢ 2 ᠲᠥᠭᠥᠷᠢᠭ ᠦᠨ ᠬᠠᠭᠤᠳ᠋ᠠᠰᠤᠨ ᠲᠤᠭᠠ ᠶᠢᠨ 4 ᠲᠠᠬᠢᠨ᠃ 1 ᠲᠥᠭᠥᠷᠢᠭ᠌᠂ 2 ᠲᠥᠭᠥᠷᠢᠭ᠌᠂ 5 ᠲᠥᠭᠥᠷᠢᠭ᠌ ᠦᠨ ᠬᠠᠭᠤᠳ᠋ᠠᠰᠤᠨ ᠵᠤᠭᠤᠰ ᠲᠤᠰ ᠲᠤᠰ ᠬᠡᠳ᠋ᠦᠢ ᠪᠠᠢᠬᠤ ᠪᠤᠢ ︖,ᠶᠠᠮᠠᠷ ᠶᠠᠮᠠᠷ ᠲᠡᠩᠴᠡᠬᠦᠦ ᠬᠤᠯᠪᠤᠠᠠᠳ᠋ᠠᠯ ᠪᠠᠢᠬᠤ ᠪᠤᠢ ︖ ᠬᠡᠷᠬᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠪᠠᠢᠭᠤᠯᠬᠤ ᠪᠤᠢ ︖,ᠠᠰᠠᠭᠤᠳ᠋ᠠᠯ ᠄,,1 ᠲᠥᠭᠥᠷᠢᠭ᠂ 2 ᠲᠥᠭᠥᠷᠢᠭ᠂ 5 ᠲᠥᠭᠥᠷᠢᠭ ᠦᠨ ᠬᠠᠭᠤᠳ᠋ᠠᠰᠤᠨ ᠲᠤᠭᠠ ᠵᠢ ᠲᠤᠰ ᠲᠤᠰ 𝑥 , 𝑦 , 𝑧 ᠬᠡᠪᠡᠯ ᠄,ᠭᠤᠷᠪᠠᠨ ᠦᠯᠦ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠦᠬᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠦᠨ ᠪᠥᠯᠥᠭ,ᠠᠰᠠᠭᠤᠳ᠋ᠠᠯ ᠄,𝑥+𝑦+𝑧=12,𝑥+2𝑦+5𝑧=22,𝑥=4𝑦,ᠬᠡᠷᠡᠯᠳ᠋ᠦ ᠳ᠋ᠦ 1 ᠲᠥᠭᠥᠷᠢᠭ᠂ 2 ᠲᠥᠭᠥᠷᠢᠭ᠂ 5 ᠲᠥᠭᠥᠷᠢᠭ ᠤᠨ ᠵᠤᠭᠤᠰ ᠨᠡᠢᠳ᠋ᠡ 12 ᠪᠤᠢ ᠂ ᠨᠡᠢᠳ᠋ᠡ 22 ᠲᠥᠭᠥᠷᠢᠭ ᠃ ᠡᠭᠦᠨ ᠳ᠋ᠦ 1 ᠲᠥᠭᠥᠷᠢᠭ᠌ ᠤᠨ ᠬᠠᠭᠤᠳ᠋ᠠᠰᠤᠨ ᠲᠤᠭᠠ ᠨᠢ 2 ᠲᠥᠭᠥᠷᠢᠭ ᠦᠨ ᠬᠠᠭᠤᠳ᠋ᠠᠰᠤᠨ ᠲᠤᠭᠠ ᠶᠢᠨ 4 ᠲᠠᠬᠢᠨ᠃ 1 ᠲᠥᠭᠥᠷᠢᠭ᠌᠂ 2 ᠲᠥᠭᠥᠷᠢᠭ᠌᠂ 5 ᠲᠥᠭᠥᠷᠢᠭ᠌ ᠦᠨ ᠬᠠᠭᠤᠳ᠋ᠠᠰᠤᠨ ᠵᠤᠭᠤᠰ ᠲᠤᠰ ᠲᠤᠰ ᠬᠡᠳ᠋ᠦᠢ ᠪᠠᠢᠬᠤ ᠪᠤᠢ ︖,① ② ③,ᠬᠢᠯᠪᠠᠷᠴᠢᠯᠠᠪᠠᠯ,ᠭᠣᠷᠪᠠᠨ ᠥᠯᠥ ᠮᠡᠳᠡᠭᠳᠡᠭᠴᠢᠳᠡᠢ ᠨᠢᠭᠡᠳᠤᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠢ ᠪᠣᠳᠣᠬᠤ,ᠭᠤᠷᠪᠠ,ᠦᠯᠦ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢ ᠵᠢ ᠨᠢ ᠤᠰᠠᠳᠬᠠᠬᠤ,ᠬᠤᠶᠠᠷ,ᠠᠷᠭᠠ ᠤᠷᠤᠯᠠᠭᠤᠯᠬᠤ,ᠠᠰᠠᠭᠤᠳ᠋ᠠᠯ ᠄,ᠠᠷᠭᠠ ᠨᠡᠮᠡᠵᠦ ᠬᠠᠰᠤᠬᠤ,,ᠪᠤᠳ᠋ᠤᠪᠠᠯ ᠄,𝑥=4𝑦= 4×2=8,ᠬᠠᠷᠢᠭᠤᠯᠳ᠋ᠠ ᠄ 1 ᠲᠥᠭᠥᠷᠢᠭ ᠂ 2 ᠲᠥᠭᠥᠷᠢᠭ ᠂ 5 ᠲᠥᠭᠥᠷᠢᠭ ᠤᠨ ᠬᠠᠭᠤᠳ᠋ᠠᠰᠤᠨ ᠲᠤᠭᠠ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ 8 , 2 , 2 ᠪᠤᠯᠤᠨᠠ ᠃,ᠦᠯᠦ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢ ᠵᠢ ᠨᠢ ᠤᠰᠠᠳᠬᠠᠬᠤ,ᠦᠯᠦ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢ ᠵᠢ ᠨᠢ ᠤᠰᠠᠳᠬᠠᠬᠤ,ᠬᠤᠷᠢᠶᠠᠩᠭᠤᠢᠯᠠᠬᠤ ᠄,ᠠᠰᠠᠭᠤᠳᠠᠯ,ᠳᠠᠷᠠᠭᠠᠬᠢ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠦᠨ ᠪᠥᠯᠥᠭ ᠢ ᠪᠣᠳᠣ᠃,3𝑥+4𝑧=7 2𝑥+3𝑦+𝑧=9 5𝑥−9𝑦+7𝑧=8,ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠭᠰᠠᠨ ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠯ,ᠬᠢᠴᠢᠶᠡᠯ ᠦᠨ ᠪᠢᠴᠢᠭ ᠦᠨ129 ᠳ᠋ᠦ᠋ᠭᠡᠷ ᠨᠢᠭᠤᠷ ᠤᠨ ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠯ ᠤᠨ ᠰᠡᠲᠤᠪ 1,ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠭᠰᠠᠨ ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠯ,ᠬᠢᠴᠢᠶᠡᠯ ᠦᠨ ᠪᠢᠴᠢᠭ ᠦᠨ129 ᠳ᠋ᠦ᠋ᠭᠡᠷ ᠨᠢᠭᠤᠷ ᠤᠨ ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠯ ᠤᠨ ᠰᠡᠲᠤᠪ 2,
ᠮᠣᠩᠭᠣᠯ ᠳ᠋ᠣᠺ ᠤᠨ ᠬᠥᠮᠥᠷᠭᠡ