8.1.2 ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳᠡᠭᠳᠡᠭᠴᠢᠳᠡᠢ ᠨᠢᠭᠡᠳᠤᠭᠡᠷ ᠵᠡᠷᠭᠡ ᠶᠢᠨ ᠲᠡᠭᠰᠢᠳᠭᠡᠯ ᠤᠨ ᠪᠥᠯᠥᠭ ᠤᠨ ᠤᠬᠠᠭᠳᠠᠬᠤᠨ

8.1 ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠪᠦᠯᠦᠭ,ᠰᠡᠳᠬᠢᠬᠥ ᠄,ᠰᠠᠭᠰᠤᠨ ᠪᠥ᠋ᠮᠪᠤᠬᠡ ᠶᠢᠨ ᠬᠤᠯᠪᠤᠭᠠᠳ᠋ᠤ ᠤᠷᠤᠯᠳ᠋ᠤᠭᠠᠨ ᠳ᠋ᠤ ᠂ ᠲᠠᠯᠠᠪᠤᠷ ᠪᠦᠷᠢ ᠶᠢᠨ ᠤᠷᠤᠯᠳ᠋ᠤᠭᠠᠨ ᠳ᠋ᠤ ᠴᠥ᠋ᠮ ᠢᠯᠠᠵᠤ ᠢᠯᠠᠭᠳ᠋ᠠᠬᠤ ᠶᠢ ᠢᠯᠭᠠᠷᠠᠭᠤᠯᠵᠤ ᠂ ᠠᠩᠬᠢ ᠪᠥ᠋ᠷᠢ 1 ᠲᠠᠯᠠᠪᠤᠷ ᠢᠯᠠᠪᠠᠯ 2 ᠬᠤᠪᠢ ᠤᠯᠭᠤᠵᠤ ᠂ 1ᠲᠠᠯᠠᠪᠤᠷ ᠢᠯᠠᠭᠳ᠋ᠠᠪᠠᠯ 1 ᠬᠤᠪᠢ ᠤᠯᠭᠤᠨ᠎᠎ᠠ ᠃ ᠨᠢᠬᠡᠨ ᠠᠩᠬᠢ10 ᠲᠠᠯᠠᠪᠤᠷ ᠤᠷᠤᠯᠳ᠋ᠤᠭᠠᠨ ᠳ᠋ᠤ ᠨᠡᠢᠳ᠋ᠡ16 ᠬᠤᠪᠢ ᠤᠯᠪᠠ ᠂ ᠲᠡᠬᠡᠪᠡᠯ ᠡᠨ᠋ᠡ ᠠᠩᠬᠢ ᠶᠢᠨ ᠢᠯᠠᠵᠤ ᠢᠯᠠᠭᠳ᠋ᠠᠭᠰᠡᠨ ᠲᠠᠯᠠᠪᠤᠷ ᠤᠨ ᠲᠤᠭ᠎᠎ᠠ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ ᠬᠡᠳ᠋ᠤᠢ ᠪᠤᠢ ︖,ᠴᠢ ᠡᠮᠤᠨ᠎᠎ᠠ ᠰᠤᠷᠤᠭᠰᠡᠨ ᠠᠷᠭ᠎᠎ᠠ ᠪᠠᠷ ᠡᠨ᠋ᠡᠬᠥ ᠠᠰᠠᠭᠤᠳ᠋ᠠᠯ ᠢ ᠰᠢᠢᠳᠪᠤᠷᠢᠯᠡᠵᠤ ᠴᠢᠳ᠋ᠠᠨ᠎᠎ᠠ ᠤᠤ︖,ᠪᠤᠳ᠋ᠤᠬᠤ ᠠᠷᠭ᠎᠎ᠠ 1 ᠄ ᠢᠯᠠᠭᠰᠡᠨ ᠲᠠᠯᠠᠪᠤᠷ ᠤᠨ ᠲᠤᠭ᠎᠎ᠠ ᠶᠢ 𝑥 ᠬᠡᠵᠤ ᠵᠢᠱᠢᠪᠡᠯ ᠂ ᠢᠯᠠᠭᠳ᠋ᠠᠭᠰᠡᠨ ᠲᠠᠯᠠᠪᠤᠷ ᠤᠨ ᠲᠤᠭ᠎᠎ᠠ ᠨᠢ (10−𝑥) ᠪᠤᠯᠤᠨ᠎᠎ᠠ ᠃ ᠲᠡᠬᠡᠪᠡᠯ 2𝑥+ (10−𝑥) = 16,ᠰᠠᠭᠰᠤᠨ ᠪᠥ᠋ᠮᠪᠤᠬᠡ ᠶᠢᠨ ᠬᠤᠯᠪᠤᠭᠠᠳ᠋ᠤ ᠤᠷᠤᠯᠳ᠋ᠤᠭᠠᠨ ᠳ᠋ᠤ ᠂ ᠲᠠᠯᠠᠪᠤᠷ ᠪᠥ᠋ᠷᠢ ᠶᠢᠨ ᠤᠷᠤᠯᠳ᠋ᠤᠭᠠᠨ ᠳ᠋ᠤ ᠴᠥ᠋ᠮ ᠢᠯᠠᠵᠤ ᠢᠯᠠᠭᠳ᠋ᠠᠬᠤ ᠶᠢ ᠢᠯᠭᠠᠷᠠᠭᠤᠯᠵᠤ ᠂ ᠠᠩᠬᠢ ᠪᠥ᠋ᠷᠢ 1 ᠲᠠᠯᠠᠪᠤᠷ ᠢᠯᠠᠪᠠᠯ 2 ᠬᠤᠪᠢ ᠤᠯᠭᠤᠵᠤ ᠂ 1ᠲᠠᠯᠠᠪᠤᠷ ᠢᠯᠠᠭᠳ᠋ᠠᠪᠠᠯ 1 ᠬᠤᠪᠢ ᠤᠯᠭᠤᠨ᠎᠎ᠠ ᠃ ᠨᠢᠬᠡᠨ ᠠᠩᠬᠢ10 ᠲᠠᠯᠠᠪᠤᠷ ᠤᠷᠤᠯᠳ᠋ᠤᠭᠠᠨ ᠳ᠋ᠤ ᠨᠡᠢᠳ᠋ᠡ16 ᠬᠤᠪᠢ ᠤᠯᠪᠠ ᠂ ᠲᠡᠬᠡᠪᠡᠯ ᠡᠨ᠋ᠡ ᠠᠩᠬᠢ ᠶᠢᠨ ᠢᠯᠠᠵᠤ ᠢᠯᠠᠭᠳ᠋ᠠᠭᠰᠡᠨ ᠲᠠᠯᠠᠪᠤᠷ ᠤᠨ ᠲᠤᠭ᠎᠎ᠠ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ ᠬᠡᠳ᠋ᠤᠢ ᠪᠤᠢ ︖,ᠡᠨ᠋ᠡ ᠠᠰᠠᠭᠤᠳ᠋ᠠᠯ ᠳ᠋ᠤ ᠬᠡᠳ᠋ᠤᠨ ᠲᠡᠩᠴᠡᠬᠥᠥ ᠬᠤᠯᠪᠤᠭᠳ᠋ᠡᠯ ᠪᠠᠢᠬᠤ ᠪᠤᠢ ︖ ᠬᠡᠳ᠋ᠤᠨ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠬᠥ ᠲᠤᠭ᠎᠎ᠠ ᠪᠠᠢᠬᠤ ᠪᠤᠢ ︖,ᠬᠡᠷᠪᠡ ᠢᠯᠠᠭᠰᠡᠨ ᠲᠠᠯᠠᠪᠤᠷ ᠤᠨ ᠲᠤᠭ᠎᠎ᠠ ᠶᠢ 𝑥 ᠬᠡᠵᠤ ᠂ ᠢᠯᠠᠭᠳ᠋ᠠᠭᠰᠡᠨ ᠲᠠᠯᠠᠪᠤᠷ ᠤᠨ ᠲᠤᠭ᠎᠎ᠠ ᠶᠢ 𝑦 ᠬᠡᠵᠤ ᠵᠢᠱᠢᠪᠡᠯ ᠂ ᠴᠢ ᠰᠡᠳ᠋ᠤᠪ ᠤᠨ ᠤᠳᠬ᠎᠎ᠠ ᠶᠢ ᠥᠨᠳ᠋ᠤᠰᠤᠯᠡᠵᠤ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠪᠠᠢᠭᠤᠯᠵᠤ ᠴᠢᠳ᠋ᠠᠨ᠎᠎ᠠ ᠦ᠋ᠦ ︖,ᠰᠡᠳ᠋ᠤᠪ ᠤᠨ ᠤᠳᠬ᠎᠎ᠠ ᠶᠢ ᠥᠨᠳ᠋ᠤᠰᠤᠯᠡᠪᠡᠯ ᠄,𝑥,𝑦,10,2𝑥,𝑦,16,ᠰᠠᠭᠰᠤᠨ ᠪᠥᠮᠪᠦᠭᠡ ᠶᠢᠨ ᠬᠤᠯᠪᠤᠭᠠᠳ᠋ᠤ ᠤᠷᠤᠯᠳ᠋ᠤᠭᠠᠨ ᠳ᠋ᠤ ᠂ ᠲᠠᠯᠠᠪᠤᠷ ᠪᠦᠷᠢ ᠶᠢᠨ ᠤᠷᠤᠯᠳ᠋ᠤᠭᠠᠨ ᠳ᠋ᠤ ᠴᠥ᠋ᠮ ᠢᠯᠠᠵᠤ ᠢᠯᠠᠭᠳ᠋ᠠᠬᠤ ᠶᠢ ᠢᠯᠭᠠᠷᠠᠭᠤᠯᠵᠤ ᠂ ᠠᠩᠬᠢ ᠪᠦᠷᠢ1 ᠲᠠᠯᠠᠪᠤᠷ ᠢᠯᠠᠪᠠᠯ 2 ᠬᠤᠪᠢ ᠤᠯᠭᠤᠵᠤ ᠂ 1ᠲᠠᠯᠠᠪᠤᠷ ᠢᠯᠠᠭᠳ᠋ᠠᠪᠠᠯ 1 ᠬᠤᠪᠢ ᠤᠯᠭᠤᠨ᠎᠎ᠠ ᠃ ᠨᠢᠬᠡᠨ ᠠᠩᠬᠢ10 ᠲᠠᠯᠠᠪᠤᠷ ᠤᠷᠤᠯᠳ᠋ᠤᠭᠠᠨ ᠳ᠋ᠤ ᠨᠡᠢᠳ᠋ᠡ16 ᠬᠤᠪᠢ ᠤᠯᠪᠠ ᠂ ᠲᠡᠬᠡᠪᠡᠯ ᠡᠨ᠋ᠡ ᠠᠩᠬᠢ ᠶᠢᠨ ᠢᠯᠠᠵᠤ ᠢᠯᠠᠭᠳ᠋ᠠᠭᠰᠡᠨ ᠲᠠᠯᠠᠪᠤᠷ ᠤᠨ ᠲᠤᠭ᠎᠎ᠠ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ ᠬᠡᠳ᠋ᠤᠢ ᠪᠤᠢ ︖,ᠪᠤᠳ᠋ᠤᠬᠤ ᠨᠢ ᠄ ᠲᠤᠰ ᠠᠩᠬᠢ ᠶᠢᠨ ᠢᠯᠠᠭᠰᠡᠨ ᠲᠠᠯᠠᠪᠤᠷ ᠤᠨ ᠲᠤᠭ᠎᠎ᠠ ᠶᠢ 𝑥 ᠬᠡᠵᠤ᠂ ᠢᠯᠠᠭᠳ᠋ᠠᠭᠰᠡᠨ ᠲᠠᠯᠠᠪᠤᠷ ᠤᠨ ᠲᠤᠭ᠎᠎ᠠ ᠶᠢ 𝑦 ᠬᠡᠵᠤ ᠵᠢᠱᠢᠪᠡᠯ,ᠢᠯᠠᠭᠰᠡᠨ ᠲᠠᠯᠠᠪᠤᠷ ᠤᠨ ᠲᠤᠭ᠎᠎ᠠ + ᠢᠯᠠᠭᠳ᠋ᠠᠭᠰᠡᠨ ᠲᠠᠯᠠᠪᠤᠷ ᠤᠨ ᠲᠤᠭ᠎᠎ᠠ = ᠪᠦᠬᠦ ᠲᠠᠯᠠᠪᠤᠷ ᠤᠨ ᠲᠤᠭ᠎᠎ᠠ,𝑥+𝑦=10,ᠢᠯᠠᠭᠰᠡᠨ ᠲᠠᠯᠠᠪᠤᠷ ᠤᠨ ᠬᠤᠷᠠᠮᠳ᠋ᠤᠯ ᠬᠤᠪᠢ + ᠢᠯᠠᠭᠳ᠋ᠠᠭᠰᠡᠨ ᠲᠠᠯᠠᠪᠤᠷ ᠤᠨ ᠬᠤᠷᠠᠮᠳ᠋ᠤᠯ ᠬᠤᠪᠢ = ᠪᠦᠬᠦ ᠬᠤᠷᠠᠮᠳ᠋ᠤᠯ ᠬᠤᠪᠢ,2𝑥+𝑦=16,ᠠᠵᠢᠭᠯᠠᠵᠤ ᠰᠡᠳᠬᠢᠬᠥ ᠄ ᠡᠨᠡ ᠬᠤᠶᠠᠷ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠨᠢ ᠨᠢᠬᠡ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠮᠥᠨ ᠤᠤ︖,2𝑥+𝑦=16 𝑥+𝑦=10,ᠡᠨᠡ ᠬᠤᠶᠠᠷ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠨᠢ ᠶᠠᠮᠠᠷ ᠬᠠᠮᠳ᠋ᠤ ᠶᠢᠨ ᠤᠨᠴᠠᠯᠢᠭ ᠲᠡᠢ ᠪᠤᠢ ︖,,ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠪᠦᠷᠢ ᠨᠢ ᠴᠥᠮ ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠬᠥ ᠲᠤᠭ᠎᠎ᠠ ᠶᠢ ᠠᠭᠤᠯᠬᠤ ᠪᠥᠭᠡᠳ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠬᠥ ᠲᠤᠭ᠎᠎ᠠ ᠠᠭᠤᠯᠤᠭᠰᠡᠨ ᠬᠡᠰᠢᠬᠥᠨ ᠦ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠤᠭ᠎᠎ᠠ ᠨᠢ ᠴᠥᠮ 1 ᠪᠤᠯᠬᠤ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠢ ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠬᠡᠨ᠎᠎ᠠ ᠃,ᠮᠠᠭᠠᠳᠯᠠᠬᠤ ᠴᠡᠭ᠌ ᠄ 1. ᠬᠡᠳ᠋ᠤᠨ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠬᠥ ᠲᠤᠭ᠎᠎ᠠ ᠲᠡᠢ ᠪᠤᠢ ︖,ᠬᠤᠶᠠᠷ,ᠮᠠᠭᠠᠳᠯᠠᠬᠤ ᠴᠡᠭ᠌ ᠄ 2. ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠬᠥ ᠲᠤᠭ᠎᠎ᠠ ᠠᠭᠤᠯᠤᠭᠰᠡᠨ ᠬᠡᠰᠢᠬᠥᠨ ᠦ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠤᠭ᠎᠎ᠠ ᠨᠢ ᠬᠡᠳ᠋ᠤᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠪᠤᠢ ︖,ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ,ᠮᠠᠭᠠᠳᠯᠠᠬᠤ ᠴᠡᠭ᠌ ᠄ 3. ᠲᠡᠩᠴᠡᠳᠬᠡᠯ ᠤᠨ ᠬᠤᠶᠠᠷ ᠲᠠᠯ᠎ᠠ ᠨᠢ ᠴᠥᠮ,ᠪᠦᠬᠦᠯᠢ ᠢᠯᠡᠷᠬᠡᠢᠯᠡᠯ,ᠬᠤᠷᠢᠶᠠᠩᠭᠤᠢᠯᠠᠯ᠄,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᠄,ᠲᠠᠷᠠᠭᠠᠬᠢ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠠᠯᠢ ᠠᠯᠢ ᠨᠢ ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠪᠥᠯᠥᠭ ᠪᠤᠯᠬᠤ ᠪᠤᠢ ︖,ᠲᠡᠬᠡᠷᠡᠬᠢ ᠠᠰᠠᠭᠤᠳ᠋ᠠᠯ ᠢᠶᠡᠷ ᠲᠠᠮᠵᠢᠨ᠂ ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠪᠥᠯᠥᠭ ᠲᠤ ᠶᠠᠮᠠᠷ ᠤᠨᠴᠠᠯᠢᠭ ᠲᠡᠢ ᠪᠠᠢᠬᠤ ᠶᠢ ᠬᠡᠯᠡᠵᠤ ᠴᠢᠳ᠋ᠠᠨ᠎᠎ᠠ ᠤᠤ︖,ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠭᠰᠠᠨ ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠯ᠄,ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠪᠦᠯᠦᠭ ᠲᠦ ᠶᠠᠮᠠᠷ ᠬᠡᠳ᠋ᠤᠨ ᠤᠨᠴᠠᠯᠢᠭ ᠲᠡᠢ ᠪᠤᠢ ︖,ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠪᠥᠯᠥᠭ ᠲᠦ ᠨᠡᠢᠳ᠋ᠡ ᠠᠳ᠋ᠠᠯᠢ ᠪᠤᠰᠤ 2 ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠬᠥ ᠲᠤᠭ᠎᠎ᠠ ᠲᠡᠢ ᠪᠥᠭᠡᠳ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠬᠥ ᠲᠤᠭ᠎᠎ᠠ ᠠᠭᠤᠯᠤᠭᠰᠡᠨ ᠬᠡᠰᠢᠬᠥᠨ ᠦ ᠬᠠᠮᠤᠭ ᠥᠨᠳ᠋ᠤᠷ ᠵᠡᠷᠬᠡ ᠨᠢ 1 ᠪᠤᠯᠤᠨ᠎᠎ᠠ ᠃ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠦᠨ ᠪᠦᠯᠦᠭ ᠨᠢ 2 ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠪᠦᠬᠦᠯᠢ ᠢᠯᠡᠷᠬᠡᠢᠯᠡᠯᠳ᠋ᠤ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠪᠤᠯᠤᠨ᠎᠎ᠠ ᠃,(2) ᠡᠩ ᠤᠨ ᠪᠠᠢᠳ᠋ᠠᠯ ᠳ᠋ᠤ ᠶᠡᠬᠡ ᠬᠠᠭᠠᠯᠳ᠋ᠡ ᠪᠠᠷ ᠬᠤᠶᠠᠷ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠢ ᠨᠡᠢᠯᠡᠬᠥᠯᠥᠨ ᠪᠢᠴᠢᠳ᠋ᠡᠭ᠌ ᠃,ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠪᠦᠯᠦᠭ ᠲᠦ 2 ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠬᠥ ᠲᠤᠭ᠎᠎ᠠ ᠲᠡᠢ ᠂ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠬᠥ ᠲᠤᠭ᠎᠎ᠠ ᠪᠥ᠋ᠷᠢ ᠶᠢ ᠠᠭᠤᠯᠬᠤ ᠬᠡᠰᠢᠬᠥᠨ ᠦ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠤᠭ᠎᠎ᠠ ᠨᠢ ᠴᠥᠮ 1 ᠪᠥᠭᠡᠳ ᠨᠡᠢᠳ᠋ᠡ ᠬᠤᠶᠠᠷ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠪᠠᠢᠨ᠎᠎ᠠ ᠂ ᠡᠢᠮᠤᠷᠬᠥᠥ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠪᠦᠯᠦᠭ ᠢ ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠪᠦᠯᠦᠭ ᠬᠡᠨ᠎᠎ᠠ ᠃,ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠬᠤᠶᠠᠷ ᠲᠠᠯ᠎ᠠ ᠶᠢᠨ ᠬᠡᠮᠵᠢᠭ᠍ᠳ᠋ᠡᠯ ᠢ ᠲᠡᠩᠴᠡᠬᠥᠯᠬᠥ ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠬᠥ ᠲᠤᠭᠠᠨ ᠦ ᠬᠡᠮᠵᠢᠭ᠍ᠳ᠋ᠡᠯ ᠢ ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠬᠠᠷᠢᠭᠤ ᠬᠡᠨ᠎᠎ᠠ ᠃,1. ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ 𝑥+𝑦=10 ᠤ ᠪᠤᠳ᠋ᠠᠳ᠋ᠡᠢ ᠠᠭᠤᠯᠭ᠎᠎ᠠ ᠲᠡᠢ ᠨᠡᠢᠴᠡᠬᠥ 𝑥 , 𝑦 ᠶᠢᠨ ᠬᠡᠮᠵᠢᠭ᠍ᠳ᠋ᠡᠯ ᠨᠢ ᠠᠯᠢ ᠠᠯᠢ ᠪᠤᠢ ︖ ᠲᠡᠳ᠋ᠡᠬᠡᠷ ᠢ ᠬᠦᠰᠦᠨᠦᠭᠲᠦ ᠳ᠋ᠤ ᠲᠠᠭᠯᠡ ᠃,ᠠᠩᠬᠠᠷ ᠄ ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠳ᠋ᠤ ᠲᠤᠭ᠎᠎ᠠ ᠥᠬᠡᠢ ᠤᠯᠠᠨ ᠬᠠᠷᠢᠭᠤ ᠲᠡᠢ ᠃,2. ᠪᠠᠰᠡ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ 2𝑥+𝑦=16 ᠤᠨ ᠪᠤᠳ᠋ᠠᠳ᠋ᠡᠢ ᠠᠭᠤᠯᠭ᠎᠎ᠠ ᠲᠡᠢ ᠨᠡᠢᠴᠡᠬᠥ ᠬᠠᠷᠢᠭᠤ ᠶᠢ ᠬᠦᠰᠦᠨᠦᠭᠲᠦ ᠳ᠋ᠤ ᠲᠠᠭᠯᠡ ᠃,,,,,,,,0,0,ᠰᠡᠳᠬᠢᠬᠥ ᠄,𝑥 + 𝑦 = 10,2𝑥 + 𝑦 = 16,ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠬᠤᠶᠠᠷ ᠲᠠᠯ᠎ᠠ ᠶᠢᠨ ᠬᠡᠮᠵᠢᠭ᠍ᠳ᠋ᠡᠯ ᠢ ᠲᠡᠩᠴᠡᠬᠥᠯᠬᠥ ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠬᠥ ᠲᠤᠭᠠᠨ ᠦ ᠬᠡᠮᠵᠢᠭ᠍ᠳ᠋ᠡᠯ ᠢ ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠬᠠᠷᠢᠭᠤ ᠬᠡᠨ᠎᠎ᠠ ᠃,6,4,6,4,ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠪᠦᠯᠦᠭ ᠤᠨ ᠬᠤᠶᠠᠷ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠶᠡᠷᠤᠩᠬᠡᠢ ᠬᠠᠷᠢᠭᠤ ᠶᠢ ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠪᠦᠯᠦᠭ ᠤᠨ ᠬᠠᠷᠢᠭᠤ ᠬᠡᠨ᠎᠎ᠠ ᠃,ᠰᠡᠳᠬᠢᠬᠥ ᠄,1. ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠬᠥ ᠲᠤᠭ᠎᠎ᠠ ᠠᠭᠤᠯᠬᠤ ᠪᠥᠭᠡᠳ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠬᠥ ᠲᠤᠭ᠎᠎ᠠ ᠠᠭᠤᠯᠤᠭᠰᠡᠨ ᠬᠡᠰᠢᠬᠥᠨ ᠦ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠤᠭ᠎᠎ᠠ ᠨᠢ ᠴᠥ᠋ᠮ 1ᠪᠤᠯᠬᠤ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠢ ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠬᠡᠨ᠎᠎ᠠ ᠃,2. ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠪᠦᠯᠦᠭ ᠲᠦ ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠬᠥ ᠲᠤᠭ᠎᠎ᠠ ᠲᠡᠢ ᠂ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠬᠥ ᠲᠤᠭ᠎᠎ᠠ ᠪᠦᠷᠢ ᠶᠢ ᠠᠭᠤᠯᠬᠤ ᠬᠡᠰᠢᠬᠥᠨ ᠦ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠤᠭ᠎᠎ᠠ ᠨᠢ ᠴᠥ᠋ᠮ 1 ᠪᠥᠭᠡᠳ ᠨᠡᠢᠳ᠋ᠡ ᠬᠤᠶᠠᠷ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠪᠠᠢᠨ᠎᠎ᠠ ᠂ ᠡᠢᠮᠤᠷᠬᠥᠥ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠪᠦᠯᠦᠭ ᠢ ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠪᠦᠯᠦᠭ ᠬᠡᠨ᠎᠎ᠠ ᠃,3. ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠬᠤᠶᠠᠷ ᠲᠠᠯ᠎ᠠ ᠶᠢᠨ ᠬᠡᠮᠵᠢᠭ᠍ᠳ᠋ᠡᠯ ᠢ ᠲᠡᠩᠴᠡᠬᠥᠯᠬᠥ ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠬᠥ ᠲᠤᠭᠠᠨ ᠦ ᠬᠡᠮᠵᠢᠭ᠍ᠳ᠋ᠡᠯ ᠢ ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠬᠠᠷᠢᠭᠤ ᠬᠡᠨ᠎᠎ᠠ ᠃,ᠬᠤᠷᠢᠶᠠᠩᠭᠤᠢᠯᠠᠯ᠄,,4. ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠪᠦᠯᠦᠭ ᠤᠨ ᠬᠤᠶᠠᠷ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠶᠡᠷᠤᠩᠬᠡᠢ ᠬᠠᠷᠢᠭᠤ ᠶᠢ ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠪᠦᠯᠦᠭ ᠤᠨ ᠬᠠᠷᠢᠭᠤ ᠬᠡᠨ᠎᠎ᠠ ᠃,5.ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠳ᠋ᠤ ᠲᠤᠭ᠎᠎ᠠ ᠥᠬᠡᠢ ᠤᠯᠠᠨ ᠬᠠᠷᠢᠭᠤ ᠲᠡᠢ ᠃ ᠬᠤᠶᠠᠷ ᠥᠯᠥ ᠮᠡᠳ᠋ᠡᠭ᠍ᠳ᠋ᠡᠭᠴᠢᠳ᠋ᠡᠢ ᠨᠢᠬᠡᠳ᠋ᠤᠬᠡᠷ ᠵᠡᠷᠬᠡ ᠶᠢᠨ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠦᠨ ᠪᠦᠯᠦᠭ ᠲᠦ ᠵᠥ᠋ᠪᠬᠡᠨ ᠨᠢᠬᠡ ᠪᠦᠯᠦᠭ ᠬᠠᠷᠢᠭᠤ ᠲᠡᠢ ᠃,ᠪᠤᠯᠪᠠᠰᠤᠷᠠᠯ ᠄,ᠬᠦᠰᠦᠨᠦᠭᠲᠦ ᠳ᠋ᠤ ᠲᠠᠭᠯᠠᠬᠤ ᠳ᠋ᠤ ᠪᠡᠨ ᠂ ᠵᠡᠬᠥᠨ ᠪᠠᠷᠠᠭᠤᠨ ᠲᠠᠯ᠎ᠠ ᠶᠢᠨ ᠨᠢᠬᠡ ᠬᠤᠤᠰ 𝑥 , 𝑦 ᠶᠢᠨ ᠬᠡᠮᠵᠢᠭ᠍ᠳ᠋ᠡᠯ ᠢ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ 3𝑥+𝑦=5 ᠶᠢᠨ ᠬᠠᠷᠢᠭᠤ ᠪᠤᠯᠭ᠎᠎ᠠ ᠃,2. ᠲᠤᠤᠷᠠᠬᠢ ᠭᠤᠷᠪᠠᠨ ᠪᠦᠯᠦᠭ ᠲᠤᠭ᠎᠎ᠠ ᠬᠡᠮᠵᠢᠭ᠍ᠳ᠋ᠡᠯ 𝑦=6 𝑥=1 ᠂ 𝑦=7 𝑥=1 ᠂ 𝑦=5 𝑥=2 ᠲᠤᠳ᠋ᠤᠷ᠎ᠠ ( ) ᠨᠢ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ 𝑥 + 𝑦 = 7 ᠶᠢᠨ ᠬᠠᠷᠢᠭᠤ ᠮᠥᠨ᠃ ( ) ᠨᠢ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ 2𝑥 + 𝑦 = 9 ᠶᠢᠨ ᠬᠠᠷᠢᠭᠤ ᠮᠥᠨ᠃ ( ) ᠨᠢ ᠲᠡᠭ᠍ᠰᠢᠳᠬᠡᠯ ᠤᠨ ᠪᠦᠯᠦᠭ 2𝑥+𝑦=9 𝑥+𝑦=7 ᠶᠢᠨ ᠬᠠᠷᠢᠭᠤ ᠮᠥᠨ᠃,5,11,3.8,1.8,−1,1.5,2,1,