CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN TĂNG THIẾT GIÁP 1 CHUYÊN ĐỀ HỆ PHƯƠNG TRÌNH BÀI TẬP GIẢI HỆ PHƯƠNG TRÌNH ĐỒNG BẬC (PHẦN 1) Bài 1. Giải các hệ phương trình sau trên tập hợp số thực 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 2 3 15, 1, 2 8. 2 3 9, 2, 2 2 2. 2 4 1, 3, 3 2 2 7. 2, 4, 2 4 2 16. 3 5 4 3, 5, 9 11 8 6. 55, 6, 24. 40, 7, x xy y x xy y x xy y x xy y x xy y x xy y x xy x xy y x xy y y xy x x y xy x xy y  + + =   + + =    + + =   + + =    − + = −   + + =    − =   + − =    − − = −   + − =    − =  =  + = ( ) ( ) 3 2 2 2 2 2 2 2 2 3 3 2 2 2 2 3 3 2 2 2 2 2 2 2 10. 2 3 , 8, 10 . 2 2 5, 9, 3 3. 7, 10, 2 3 16. 2 15, 11, 8 35. 2 3 4 1, 12, 2 1. 3 4, 13, 4 1. 14, y xy x y x y x x x y y x xy y x xy y y x x y xy x y xy x y x y xy x y y xy x xy y      + =    − =   + =    + + =   − + =    − =   + =    + =   + =    + = +   = +    − =   − + =   2 2 2 2 3 2 11, 2 3 17. x xy y x xy y  + + =   + + =   2 2 2 2 2 2 2 2 2 2 2 2 3 3 2 2 3 3 3 2 2 3 3 2 2 2 2 2 4 1 0, 15, 3 2 2 7. 2 3 9, 16, 4 5 5. 3, 17, 6 5 4 15. 3 5, 18, 3 4 7. 5, 19, 2 3. 2 2 , 20, 3 . x xy y x xy y x xy y x xy y x xy y x xy y x y xy xy y x y xy xy x y x y x y x y x y  − + + =   + + =    − + =   − + =    + + =   + + =    + + =   + =    + + + =   + =    + = +   − = +  2 2 2 2 2 2 2 2 3 3 2 3 3 3 2 2 3 3 2 2 3 3 2 2 3 3 3 2 3 2 4 , 21, 3 3 3 5 . 5 7, 22, 3 4. 3 4 0, 23, 2 3 . 2, 24, 2 2 . 3 4, 25, 3 5 2 6 . 2, 26, 5 2 4 3 . 2 27, x y y x x y xy y x x y yx x y x y xy y x y x y x x y x y x x y y x x y x y x y x y x   − + =   + + = +    + + =   + =    + − =   + =    + =   + = +    + =   + − =    + =   + = +   + 3 3 3 2 2 2 2 3 6, 2 3 5. 15, 28, 10. 3 4, 29, 4 5. y x y x xy y xy x xy y xy  + =   + =    + =   + =    + =   + =   CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN TĂNG THIẾT GIÁP 2 Bài 2. Giải các hệ phương trình sau trên tập hợp số thực ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 3 2 3 2 2 2 2 2 2 2 2 2 2 3 5, 1, 3 5. 3 2 1 , 2, 2 3. 2 3, 3, 2. 3 2, 4, 2 1. 3 2, 5, 2 1. 2 1, 6, 3 2. 3 1, 7, 1. 3 2 8, x xy y xy y x x x y y x y x x y y y x x x x y y y x x x y y x y y x y x x y x y yx x y xy x xy y  + + =   + + =    + = +   + =    + =     + =   − =   − =    − =   − =    − =   − =    + = +   − = −   + − ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2, 2 3. 3 2, 9, 4 3 . 3 , 10, 2 3 6 1. 3 4 , 11, 3 4 0. 2 4 2 1, 12, 4 5 3 4. 3 5 3 , 13, 4 3 . 3 14, x x y x x y y y x y x y x y xy x xy y x y x x y y x y y xy xy y y x y x y x x y x xy y x x y x y  =   + =    − =   = −    + = +   + = −    + = + −   − + =    − = − −   = + −    + = + + +   + + = +   + ( ) ( ) 2 2 2 2 2 2 2 2 4 , 4 5 2 3. 4 7 3 4, 15, 2 3 26. x y y x x yx y x y x x y  =   = + −    + + = + −   + + =   ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( )( ) 2 2 2 2 2 2 2 2 2 2 4 1, 16, 6 6. 2 4 5, 17, 3 4 3 8. 3 4 7 3 2 , 18, 5 5 3 7 0. 2 2 2 1, 19, 6 8 1. 3 2 2 1, 20, 3 2 6. 2 3 , 3 2 21, 1 5 x y x y y y x y x x x y y x y xy y y x x xy x x y x xy y x y y x y x xy xy x y x y x y x y x y x y x y  + − =   − + =    + − + =   + + + − =    + = −   + − − =    − + − =   + = −   − − =    − + = −   − = − − = ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 3 3 2 2 3 3 2 2 4 2 4 2 2 . 5 2 4 3 , 22, 5 4 . 2 1 , 23, 4 3 . 4 3 , 24, 2 0. 3 1 0, 25, 2 3 4. 5, 26, 1. 13, 27, 468. 28, x y x y x y y x y x x x y y x x x y x y x y y x x x x y y y y x x y xy x y x y x y y x x y y x       −  − =   − =    − =     − =    − =   − + =    + − + =   + − =    + =   + =    + + + =   + =   ( ) ( )( ) 3 3 5 5 2 2 3 3 3 3 2 2 1, . 7, 29, 2. 2 9 2 3 , 30, 3. x y x y x y x y xy x y x y x y xy x xy y  + =   + = +    − =   − =    − = − +   − + =   CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN TĂNG THIẾT GIÁP 3 Bài 3. Giải các hệ phương trình sau trên tập hợp số thực ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 3 3 2 2 3 3 2 2 3 3 2 2 3 2 3 2 2 3 3 , 1, 7 . 8 2 , 2, 3 3 1 . 4 16, 3, 1 5 1 . 2 3 1, 4, 2 3. 5, 5, 2 5 2 0. 2 2000 0, 6, 500 . 2 2 7, x xy y x y x xy y x y x x y y x y x y y y x x y x y x xy y y x x y xy x xy y y yx x x y x y  − + = −   + + = −    − = +   − = +    + = +   + = +    + =   − =    + − =   − + + =    − + =   − =   − + ( ) ( ) ( ) ( ) ( ) 2 2 2 2 3 3 2 3 3 2 2 5 5 3 3 2 2 3 2 2 2 3 3 3 3 3 3 3 3, 2 2 1. 9, 8, 7. 4, 9, 2. 3 0, 10, 2 0. 31 , 7 11, 3. 3 , 12, 3 1. 2 , 13, 3 . 1 14, y x x y y x y x y x x y x y xy y x y x xy y x y x y x xy y x xy y x y x y xy x y x y y x  =   − − =    + =   − =    + =   + =    + + − =   + − =    + =  +   + + =   + =   + =    + =   + =   − = 5 5 2 2 3 , 0. 1, 15, 2 . x y xy x y xy x x y    − + =    + − =   = +   ( ) 2 2 3 3 3 3 2 2 3 3 2 3 2 2 2 5 5 3 3 2 2 10 10 8 8 2 2 2 2 3, 16, 2 2 . 1, 17, 2 3. 3 20, 18, 3 7. 5, 19, 11 11 . 9, 20, 6. 1, 21, . 3 2 11, 22, 5 x y xy x y y x x y x y xy y x x y y y x x y x y x y x y xy x y x y x y x y x xy y x xy y  + + =   + = +    + =   + + =    + =   + =    + =   + = +    + =   + =    + =   + = +   + + = + + ( ) ( ) ( ) 2 2 2 2 3 2 3 2 3 3 2 4 4 3 2 3 4 4 2 2 2 2 3 3 2 2 25. 6 2 56, 23, 5 49. 2 3 5, 24, 6 7. 1, 25, 4 4 . 4 8 1, 26, 2 8 2 . 1 2 4 2 , 27, 2 . 4 2 , 28, 1 3 1 x xy y x xy y x x y y xy x y xy x y x y x xy y x y x y x y y x y x xy y x x y x y x y    =    − − =   − − =    + =   + =    + − =   + = +    − + =   + = +    − = +   + − =   − = + − = − 3 2 2 2 2 2 3 3 2 2 2 2 2 2 . , 29, 3 5. 2 4, 30, 2 5 . 4 , 31, 2 3 7 . x x y x y x y xy x xy y x y xy x y x x xy x y y y xy x y x       + = +   + + =    + + =   + + + =    + + + =   + + + =   CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN TĂNG THIẾT GIÁP 4 Bài 4. Giải các hệ phương trình sau trên tập hợp số thực ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 , 1, 3 6 1. 3 4 0, 2, 5 9 15 . 2 5 2 0, 3, 8 7 1. 2 , 4, 3 2 2 7 . 2 4 , 5, 4 5. 2 2 , 6, 3 4. x y xy x y xy x xy y x y xy x xy y x y x y x y xy x y x y xy x x y x y xy x y xy x y xy x y x y  + =   + = −    + − =   + + =    − + =   + = + +    + + = +   + + =    − + + =   + + =    − + = −   + = ( )( ) ( )( ) ( )( ) ( )( ) ( ) ( ) ( ) 2 2 2 2 2 2 3 3 3 2 2 2 2 3 2 , 7, 3 3 2 2 . 2 6 , 8, 3 4 20 . 2 3 5 , 9, 2 . 5 2 2, 10, 4 3 . 2 1, 11, 2 2 . 3 3 , 12, 3 3. 2 1 0, 13, x y x y xy x y x y xy x y x y xy x y x y xy x x y y y x y x x y xy y x xy y x x y y x x x y x xy y xy x xy   − − =   − − =   + + =   + + =   + =   + =    = − −   = −    − =   − = −    + = +   − = −   + = ( ) ( ) ( ) ( ) ( ) ( ) ( ) 3 3 2 2 2 2 2 3 3 2 2 2 2 8 9 0. 13, 14, 25. 2, 15, 19. 4 3 , 16, 2. x y x y x y x y x y x y x y y x y xy x y x y    − + − =    − + =   + − =    − =   − =    − =   + =   3 2 3 2 2 3 2 3 2 2 3 2 3 2 2 2 3 3 2 2 3 2 3 2 2 2 3 3 2 2 2 , 17, 2 3 7 . 16 2 , 18, 3 5 . 2 3 , 19, 3 . 2 3 , 20, 3 . 3 4 , 21, 2 3 . 4 3 0, 22, . 4 23, x xy y x y x y xy x xy y x y xy x y xy x x x y y xy x y x xy y y y xy x x y x xy x y x y xy x x  = +   + + + =    = +   + + =    + =   + + =    = −   + + =    + =   + =    − + =   + = +   ( ) ( ) ( ) 3 2 2 3 2 2 2 3 2 2 3 2 2 3 2 2 3 2 2 3 2 2 2 3 2 3 2 2 2 2 2 2 2 , 1 3 . 4 , 24, 2 3 . 5 3 , 25, 3 2 3. 3 5 0, 26, 7 8 18 2 . 3 5 , 27, 3 5 . 3 2 , 28, 9 x y xy y x y xy x y x y x x y x x y xy y xy x y y xy x y x xy x y x xy y x y x x y x y xy x x y y y x x  = + +   + + =    = +   + =    = + +   + = + +    + + − =   + = − −    + + =   + + + =   − = + ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 3 2 3 2 2 3 3 2 2 3 2 2 3 2 2 20 12 13 4 . 3 2 2 , 29, 4 1 2 2 1 . 6 4 , 30, 2 2. 5 2 6 , 31, 2 2 8. 6 5 3 2 , 32, 3 . y x y x x x y y y x x y y x x x y x xy y x x y x y xy y x x xy y x y x x y xy y x y xy x    + = + +    − = +   − = + +    = + +   + − =    + = +   + + + + =    = + −   + = +   CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN TĂNG THIẾT GIÁP 5 Bài 5. Giải các hệ phương trình sau trên tập hợp số thực ( ) ( ) ( ) 3 2 2 3 2 3 2 2 2 3 2 2 3 2 2 3 3 2 2 3 3 2 2 3 3 2 2 2 2 2 6 4 , 1, 2 4. 6 2 3 , 2, 3 1 . 6 3 2 , 3, 4. 3 4 5 6 0, 4, 5. 5 3 7 , 5, 4 3 . 6 3 6, x x y xy y x y x x xy x y xy y x y y x x y xy y x y xy x y xy x y y x x y xy x y x y xy x y x y x xy y x y xy  = + +   + + =    + = + +   = + −    = + +   + + + =    + + − =   + + + + =    + = +   + = + −   − ( ) ( ) ( ) 2 3 3 2 2 2 3 3 2 2 3 3 3 3 2 3 3 3 3 2 2 3 3 3 3 2 2 3 2 2 3 3 2 5 , 2. 6 4 3 , 7, 2 5. 7 3 , 8, 4 6. , 9, 3 6. 10 4 5 , 10, 1 2 3 . 10 5 4 , 11, y x x y x y y x xy x y xy x x xy x y y x y x y x y x y x y x x y x x y xy y x x y y x x y xy y x y x y x y  + =   + =    + = +   + + + =    = + +   + + =    = + −   + + + =    = + +   + + − =   = + + + + + + + 3 2 2 3 2 2 3 3 2 2 3 2 2 3 3 2 2 2 2 3 3 2 2 2 2 3 2 2 3 3 2 2 2 6. 8 6 , 12, 4 . 9 7 , 13, 3 . 7 4 2 , 14, 4 . 3 2 2 , 15, 2 5 . 2 5 4 , 16, 3 . x x y xy y x x y y y y x y xy x x x y xy y x x y xy x y x y xy x y x y xy x x y xy y x x y xy y x xy xy y    =    = + +   + + + =    = + +   + + =    − = +   + + + =    = − +   + + = −    = − +   + + =   3 3 2 2 2 3 2 2 2 2 3 3 2 2 2 2 2 2 3 3 2 3 2 3 2 2 2 3 2 2 3 2 , 17, 2 3. 7 9 2 , 18, 3 1. 4 2 , 19, 3 4 8 . 4 2 , 20, 2 4 . 3 7 8 2 , 21, 1 4 . 5 3 0, 22, 2 x y x y xy x y x x y xy x y xy x y xy x y x xy y y x y xy x y x y y x xy y x y x x y y x xy xy y y  + = +   + =    = −   + = −    − = +   + + =    + = −   + + =    + = +   + + + =   − + + = + 2 3 3 2 2 2 2 3 3 2 2 2 2 3 3 2 2 2 3 3 3 2 2 2 2 3 3 2 2 2 2 1 2 2 . 10 2 9 , 23, 3 4 . 3 7 5 , 24, 3 . 4 3 6 , 25, . 3 5 , 26, 4 . 6 4 , 27, 3 4 5 12 . x x y x y x y xy x y y x y x y xy x x y y x y x y xy x x y y x y x y xy x x y y xy x y x y xy x y xy x    + = +    + = +   + =    − = −   + + =    − = −   + = +    + = −   + + + =    − = +   + + =  ( ) ( ) 3 3 2 2 2 2 2 2 2 2 2 2 2 3 2 2 2 2 3 3 2 2 3 7 5 , 28, 2 3 4 10 . 5 6 , 29, 3 . 3 7 10 , 30, 2 4. 4 2 3 , 31, 3 . 5 8 4 , 32, 3 5 . xy x y x y x x y y xy x y xy x x xy y x xy y x y x xy x x y y x x y xy x y xy x y y xy y x   − = −   + + + =    + =   + + =    + =   + + =    = − −   + + =    − = −   + + =   CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN TĂNG THIẾT GIÁP 6 Bài 6. Giải các hệ phương trình sau trên tập hợp số thực ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 10 , 1, 2 8. 3 3 9 10 3 , 2, 1 3 0. 3 2 2 2 4, 3, 3 5 2. 3 3 9 5 1, 4, 2 5 . 3 4 5 8 , 5, 6 1 3 7 . 2 2 2 2 6, x y xy x x y x y x y x y x y x y x x xy y x x xy y x y xy y x xy y x y x y xy x y y x xy x x y  + =   + + =    + − − = −   + + =  −   + + + =   + + + =    + + = + −   + = +    + + + = +   − + + =   − + ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 5 4 , 3 2 4 5 11 . 2 3 2 1 2 4 2 0, 7, 2 2 3 2 1. 3 1 2 1 0, 8, 3 2 . 2 3 8 6 4 , 9, 2 2 3 1. 5 7 1 5 , 10, 4 3 1. x y x y x y x y xy x x y y y x x y x x y y x y xy x x x xy x y y y x yx y x x y y x x y x xy xy  + = −   + = + +    + − + + + + + =   + = + +    − + + + =   = + −    − − − − + = +   + + = +    + + + = +   + = +  ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 8 9 2 1 9 , 11, 2 4 . 7 8 1 2 8 , 12, 3 4. 1 2 2 1 , 13, 2 4 2 5 2 . 2 1 3 , 14, 3 5 . 3 2 , 15, 2. 16, x y xy x y x x xy y x y y x xy xy x y x x x y y x x xy x x y x y x xy x x y x xy x xy x xy y x y x y x   + − + + =   + + =    + + + = +   + + = +    + = + − +   + + = +    + + + = + + +   + + =    − + = −   + =   2 2 2 2 2 2 0, 1. x xy y y x y  + − − − =   + =   ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( )( ) ( )( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 1 1 4, 17, 2 1 3 1 2 . 3 1 2 4, 18, 3 2 4 1 4. 3 4 1 , 19, 3 7 11 . 2 2 3 1 2 0, 20, 2 4 4 1 2 2 0. 2 3 2 2 21, y y x x x y y x x x x y x y y x y y x y x xy y x x y x x y xy x y x y x y x x y y x y x y x y x  + − + − =   + − = + −    + + + + =   + + + + =    + − = − −   + + =    + + + + + + =   + + + + + + + =   − − + + − ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 2 3 3 2 3 4 0, 2 3 3 5. 2 1 3 4 . 22, 2 4 1, 2 3 4 , 23, 4 3 2 . 2 3 3 3 , 24, 2 3 5 . 2 2 , 25, 2 4 . 2 3 2 26, y x y x y x y x y x y x y x y x x y x y xy x y x y x y xy y x x y x xy y y x x y xy x x y xy y x y y x  =   + + + − =  − +   − + + = −   + + = +  − +   + + = +   + = +    + + = +   + + = +    + = +   + = −   − = − 3 2 2 3 3 2 2 2 4 4 3 3 2 4 4 2 2 2 2 3 3 2 2 2 2 4 4 3 3 2 , 2 1. 2 3 3 , 27, 3 3. , 28, 2 4. 2 3 , 29, 3 3. 2 2 5 , 30, 3 2 2. 5 3 , 31, 2 2. 2 32, x y x y x y xy x y xy x y x y x y xy x y x xy y x yx y x y xy x y x y x xy y x y x y x y xy    − =    + = + +   + − =    + = +   + + =    + = − +   + − =    + + + = +   + − =    + = −   − + =   3 2 2 2 2 2 2 3 , 2 2 5. x y x xy x y x xy y  + + = +   + + =   . MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN TĂNG THI T GIÁP 1 CHUYÊN ĐỀ HỆ PHƯƠNG TRÌNH BÀI TẬP GIẢI HỆ PHƯƠNG TRÌNH ĐỒNG BẬC. BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN 1 – SƯ ĐOÀN 4 – QUÂN ĐOÀN TĂNG THI T GIÁP 2 Bài 2. Giải các hệ phương trình sau trên tập hợp số thực