8.1.1 ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳᠡᠭᠳᠡᠭᠴᠢᠳᠡᠢ ᠨᠢᠭᠡᠳᠤᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠤᠨ ᠤᠬᠠᠭᠳᠠᠬᠤᠨ
ᠠᠯᠪᠠᠨ ᠵᠢᠷᠤᠮ ᠤᠨ ᠰᠤᠷᠭᠠᠨ ᠬᠦᠮᠦᠵᠢᠯ ᠦᠨ ᠰᠤᠷᠬᠤ ᠪᠢᠴᠢᠭ,ᠳᠣᠯᠣᠳᠤᠭᠠᠷ ᠣᠨ( ᠳᠣᠣᠷᠠᠳᠤ),,,ᠬᠢᠴᠢᠶᠡᠯᠯᠡᠭᠴᠢ᠄ ᠬᠠᠰᠪᠤᠶᠠᠨᠳᠤ,8.1.1 ᠬᠤᠶᠠᠷ ᠦᠯᠦ ᠮᠡᠳᠡᠭᠳᠡᠭᠴᠢᠳᠡᠢ ᠨᠢᠭᠡᠳᠤᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠦᠨ ᠪᠦᠯᠦᠭ,ᠰᠠᠭᠰᠤᠨ ᠪᠥᠮᠪᠦᠭᠡ ᠶᠢᠨ ᠬᠤᠯᠪᠤᠭᠠᠳᠤ ᠤᠷᠤᠯᠳᠤᠭᠠᠨ ᠳᠤ᠂ ᠲᠠᠯᠠᠪᠤᠷ ᠪᠦᠷᠢ ᠳᠤ ᠴᠥᠮ ᠢᠯᠠᠵᠤ ᠢᠯᠠᠭᠳᠠᠬᠤ ᠶᠢ ᠢᠯᠭᠠᠷᠠᠭᠤᠯᠵᠤ᠂ ᠠᠩᠭᠢ ᠪᠦᠷᠢ 1 ᠲᠠᠯᠠᠪᠤᠷ ᠢᠯᠠᠪᠠᠯ 2 ᠬᠤᠪᠢ ᠣᠯᠭᠤᠵᠤ᠂1 ᠲᠠᠯᠠᠪᠤᠷ ᠢᠯᠠᠭᠳᠠᠪᠠᠯ 1 ᠬᠤᠪᠢ ᠣᠯᠭᠤᠨᠠ᠃ ᠨᠢᠭᠡᠨ ᠠᠩᠭᠢ 10 ᠲᠠᠯᠠᠪᠤᠷ ᠤᠷᠤᠯᠳᠤᠭᠠᠨ ᠳᠤ ᠨᠡᠢᠲᠡ 16 ᠬᠤᠪᠢ ᠣᠯᠪᠠ᠃,ᠠᠬᠤᠢ ᠪᠠᠢᠳᠠᠯ ᠤᠨ ᠬᠥᠲᠥᠯᠥᠯᠲᠡ,ᠢᠯᠠᠬᠤ,ᠢᠯᠠᠭᠳᠠᠬᠤ,ᠲᠠᠯᠠᠪᠤᠷ ᠤᠨ ᠲᠣᠭᠠ,ᠬᠣᠷᠠᠮᠳᠤᠯ ᠬᠤᠪᠢ,ᠨᠠᠢᠲᠡ,ᠰᠠᠭᠰᠤᠨ ᠪᠥᠮᠪᠦᠭᠡ ᠶᠢᠨ ᠬᠤᠯᠪᠤᠭᠠᠳᠤ ᠤᠷᠤᠯᠳᠤᠭᠠᠨ ᠳᠤ᠂ ᠲᠠᠯᠠᠪᠤᠷ ᠪᠦᠷᠢ ᠳᠤ ᠴᠥᠮ ᠢᠯᠠᠵᠤ ᠢᠯᠠᠭᠳᠠᠬᠤ ᠶᠢ ᠢᠯᠭᠠᠷᠠᠭᠤᠯᠵᠤ᠂ ᠠᠩᠭᠢ ᠪᠦᠷᠢ 1 ᠲᠠᠯᠠᠪᠤᠷ ᠢᠯᠠᠪᠠᠯ 2 ᠬᠤᠪᠢ ᠣᠯᠭᠤᠵᠤ᠂1 ᠲᠠᠯᠠᠪᠤᠷ ᠢᠯᠠᠭᠳᠠᠪᠠᠯ 1 ᠬᠤᠪᠢ ᠣᠯᠭᠤᠨᠠ᠃ ᠨᠢᠭᠡᠨ ᠠᠩᠭᠢ 10 ᠲᠠᠯᠠᠪᠤᠷ ᠤᠷᠤᠯᠳᠤᠭᠠᠨ ᠳᠤ ᠨᠡᠢᠲᠡ 16 ᠬᠤᠪᠢ ᠣᠯᠪᠠ᠃,ᠠᠬᠤᠢ ᠪᠠᠢᠳᠠᠯ ᠤᠨ ᠬᠥᠲᠥᠯᠥᠯᠲᠡ,ᠢᠯᠠᠬᠤ,ᠢᠯᠠᠭᠳᠠᠬᠤ,ᠲᠠᠯᠠᠪᠤᠷ ᠤᠨ ᠲᠣᠭᠠ,ᠬᠣᠷᠠᠮᠳᠤᠯ ᠬᠤᠪᠢ,ᠨᠠᠢᠲᠡ,ᠨᠢᠭᠡ ᠰᠢᠩᠬᠢᠯᠢᠭ ᠲᠦ ᠳᠠᠬᠢᠶᠠ ᠲᠠᠤᠯᠠᠢ ᠨᠠᠢᠲᠡ 12 ᠪᠣᠢ᠂ ᠬᠥᠯ ᠦᠨ ᠲᠣᠭᠠ ᠨᠢ 32 ᠪᠠᠢᠪᠠᠯ᠂ ᠬᠡᠳᠤᠨ ᠲᠠᠤᠯᠠᠢ ᠬᠡᠳᠤᠨ ᠳᠠᠬᠢᠶᠠ ᠪᠠᠢᠬᠤ ᠶᠢ ᠲᠠᠭᠠᠮᠠᠭᠯᠠᠵᠤ ᠦᠵᠡ᠃,ᠠᠬᠤᠢ ᠪᠠᠢᠳᠠᠯ ᠤᠨ ᠬᠥᠲᠥᠯᠥᠯᠲᠡ,ᠳᠠᠬᠢᠶᠠ,ᠲᠠᠤᠯᠠᠢ,ᠲᠣᠯᠣᠭᠠᠢ,ᠬᠥᠯ,ᠨᠠᠢᠲᠡ,ᠠᠰᠠᠭᠤᠳᠠᠯ 1,①𝑥+𝑦=10 ② 2𝑥+𝑦=16 ③ 𝑥+𝑦=12 ④ 4𝑥+2𝑦=32,ᠳᠠᠷᠠᠭᠠᠬᠢ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠢ ᠶᠠᠭᠠᠬᠢᠵᠤ ᠨᠠᠷᠠᠢᠳᠪᠡᠯ ᠵᠣᠬᠢᠰᠲᠠᠢ ᠪᠣᠢ ︖,ᠳᠠᠷᠠᠭᠠᠬᠢ ᠢᠯᠡᠷᠭᠡᠢᠯᠡᠯ ᠡᠴᠡ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠪᠣᠯᠬᠤ ᠨᠢ ᠄,ᠰᠠᠭᠤᠷᠢ ᠮᠡᠳᠡᠯᠭᠡ,① 2𝑥 ② 2𝑥−80 ③ 120𝑥−232=8,ᠥᠯᠥ ᠮᠡᠳᠡᠬᠦ ᠲᠣᠭᠠ ᠠᠭᠤᠯᠤᠭᠰᠠᠨ ᠲᠡᠩᠴᠡᠳᠭᠡᠯ,ᠰᠠᠭᠤᠷᠢ ᠮᠡᠳᠡᠯᠭᠡ,ᠳᠠᠷᠠᠭᠠᠬᠢ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠡᠴᠡ ᠨᠢᠭᠡ ᠥᠯᠥ ᠮᠡᠳᠡᠭᠳᠡᠭᠴᠢᠳᠡᠢ ᠨᠢᠭᠡᠳᠤᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠪᠤᠯᠬᠤ ᠨᠢ ᠄,① 1 𝑥 −12=12 ② 𝑥 2 −8=8 ③ 12𝑥+2=3,ᠨᠢᠭᠡ ᠥᠯᠥ ᠮᠡᠳᠡᠬᠦ ᠲᠣᠭᠠ ᠠᠭᠤᠯᠬᠤ ᠪᠥᠭᠡᠳ ᠥᠯᠥ ᠮᠡᠳᠡᠬᠦ ᠲᠣᠭᠠ ᠠᠭᠤᠯᠤᠭᠰᠠᠨ ᠭᠡᠰᠢᠬᠦᠨ ᠦ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠣᠭᠠ ᠨᠢ 1,ᠨᠢᠭᠡ ᠥᠯᠥ ᠮᠡᠳᠡᠭᠳᠡᠭᠴᠢᠲᠡᠢ ᠨᠢᠭᠡᠳᠦᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠦᠨ ᠣᠨᠴᠠᠯᠢᠭ᠄ ① ᠨᠢᠭᠡ ᠥᠯᠥ ᠮᠡᠳᠡᠬᠦ ᠲᠣᠭᠠ （ᠥᠯᠥ ᠮᠡᠳᠡᠭᠳᠡᠭᠴᠢ）ᠠᠭᠤᠯᠤᠨᠠ᠃ ② ᠥᠯᠥ ᠮᠡᠳᠡᠬᠦ ᠲᠣᠭᠠᠨ ᠤ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠣᠭᠠ ᠴᠥᠮ 1 (ᠵᠡᠷᠭᠡ)᠃ ③ ᠴᠥᠮ ᠪᠦᠬᠦᠯᠢ ᠢᠯᠡᠷᠬᠡᠢᠯᠡᠯ （ᠬᠤᠪᠢᠶᠠᠷᠢ ᠳᠤ ᠨᠢ ᠥᠯᠥ ᠮᠡᠳᠡᠬᠦ ᠲᠣᠭᠠ ᠠᠭᠤᠯᠬᠤ ᠦᠭᠡᠢ）᠃,ᠠᠰᠠᠭᠤᠳᠠᠯ 1,①𝑥+𝑦=10 ② 2𝑥+𝑦=16 ③ 𝑥+𝑦=12 ④ 4𝑥+2𝑦=32,ᠳᠠᠷᠠᠭᠠᠬᠢ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠢ ᠶᠠᠭᠠᠬᠢᠵᠤ ᠨᠠᠷᠠᠢᠳᠪᠡᠯ ᠵᠣᠬᠢᠰᠲᠠᠢ ᠪᠣᠢ ︖,𝑥,𝑦,𝑥,𝑦,𝑦,𝑦,𝑥,𝑥,1,1,1,1,1,1,1,1,ᠬᠣᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳᠡᠭᠳᠡᠭᠴᠢᠳᠡᠢ ᠨᠢᠭᠡᠳᠤᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ,ᠬᠣᠶᠠᠷ ᠦᠯᠦ ᠲᠣᠭᠠ ᠠᠭᠤᠯᠤᠭᠰᠠᠨ ᠪᠥᠭᠡᠳ ᠦᠯᠦ ᠮᠡᠳᠡᠬᠦ ᠲᠣᠭᠠ ᠠᠭᠤᠯᠤᠭᠰᠠᠨ ᠭᠡᠰᠢᠭᠦᠨ ᠤ᠌ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠣᠭᠠ ᠨᠢ ᠨᠢᠭᠡ ᠪᠣᠯᠬᠤ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ( ᠪᠠᠰᠠ ᠲᠡᠡᠭᠴᠡᠭᠥᠥ ᠲᠡᠮᠳᠡᠭ ᠤᠨ ᠬᠣᠶᠠᠷ ᠲᠠᠯᠠ ᠨᠢ ᠴᠥᠮ ᠪᠦᠬᠦᠯᠢ ᠢᠯᠡᠷᠬᠡᠢᠯᠡᠯ ) ᠪᠣᠯᠬᠤ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠢ ᠬᠣᠶᠠᠷ ᠦᠯᠦ ᠮᠡᠳᠡᠭᠳᠡᠭᠴᠢᠳᠠᠢ ᠨᠢᠭᠡᠳᠣᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠭᠡᠨᠡ᠃,ᠬᠤᠷᠢᠶᠠᠩᠭᠤᠢᠯᠠᠯ,ᠨᠢᠭᠡ ᠥᠯᠥ ᠮᠡᠳᠡᠭᠳᠡᠭᠴᠢᠲᠡᠢ ᠨᠢᠭᠡᠳᠦᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠬᠡᠯ ᠦᠨ ᠣᠨᠴᠠᠯᠢᠭ᠄ ① ᠬᠣᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳᠡᠬᠦ ᠲᠣᠭᠠ （ᠥᠯᠥ ᠮᠡᠳᠡᠭᠳᠡᠭᠴᠢ）ᠠᠭᠤᠯᠤᠨᠠ᠃ ② ᠥᠯᠥ ᠮᠡᠳᠡᠬᠦ ᠲᠣᠭᠠᠨ ᠤ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠣᠭᠠ ᠴᠥᠮ 1 (ᠵᠡᠷᠭᠡ)᠃ ③ ᠴᠥᠮ ᠪᠦᠬᠦᠯᠢ ᠢᠯᠡᠷᠬᠡᠢᠯᠡᠯ （ᠬᠤᠪᠢᠶᠠᠷᠢ ᠳᠤ ᠨᠢ ᠥᠯᠥ ᠮᠡᠳᠡᠬᠦ ᠲᠣᠭᠠ ᠠᠭᠤᠯᠬᠤ ᠦᠭᠡᠢ）᠃,ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠭᠰᠠᠨ ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠯ,,1.ᠳᠣᠣᠷᠠᠬᠢ ᠢᠯᠡᠷᠬᠡᠢᠯᠡᠯ ᠳ᠋ᠤ ᠬᠤᠶᠠᠷ ᠦᠯᠤ ᠮᠡᠳ᠋ᠡᠭᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠭᠡᠳ᠋ᠤᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠢᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠪᠤᠯᠬᠤ ᠨᠢ ( ),① 3𝑥+2𝑦−1 ② 2(2−𝑥)+3𝑦+5=0 ③ 3𝑥−4𝑦=𝑧 ④ 𝑥+𝑥𝑦=1 ⑤ 𝑦²+3𝑦=5𝑥 ⑥ 4𝑥−𝑦=0 ⑦ 2𝑥−3𝑦+1=2𝑥+5,ᠲᠤᠤᠷᠠᠬᠢ ᠲᠡᠩᠴᠡᠳᠬᠡᠯ ᠢ ᠬᠠᠪᠰᠤᠷᠴᠤ ᠥᠪᠡᠷ ᠤᠨ ᠬᠡᠷ ᠢ ᠨᠢ ᠤᠯᠵᠤ ᠥᠭ᠍ᠬᠥᠬᠡᠷᠡᠢ ᠃,(1) 𝑥+𝑦=11,(2) 𝑚+1=2,(3) 𝑥2+𝑦=5,(4) 3𝑥－𝜋=11,(5) －5𝑥=4𝑦+2,(6) 7+𝑎=2𝑏+11𝑐,(7) 7𝑥+ 2 𝑦 =13,ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠪᠣᠯᠬᠤ ᠨᠢ,ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠪᠢᠰᠢ ᠨᠢ,ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠭᠰᠠᠨ ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠯ,
ᠮᠣᠩᠭᠣᠯ ᠳ᠋ᠣᠺ ᠤᠨ ᠬᠥᠮᠥᠷᠭᠡ