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CHUYÊN ĐỀ HỆ PHƯƠNG TRÌNH BÀI TẬP GIẢI HỆ PHƯƠNG TRÌNH CƠ BẢN (PHẦN 2) Bài Giải hệ phương trình sau tập hợp số thực x + xy + x = 10, 1, y + xy + y = 20 x − xy + x − y + y = 0, 16, 2 x + y = xy + x − xy + x = 2, 2, y + 3xy + y = x + y + xy = 3, 17, 2 x + y + xy + x + y = 2 x − xy + y = 2, 3, 2 y + xy + 3x = 12 x − xy + y = 2, 18, 2 x − xy + y + x = y − x + x = xy + y − 1, 19, x + xy + x = x ( x − y + 3) = 1, 4, y ( y + x + 3) = x ( x − y + 3) = 3, 5, y ( y − x − 3) = −3 3 x − xy + y + x = 5, 8, 2 x − xy + y = y − x − xy + = y − x, 20, 2 x + y = y − xy + = x − y, 21, 2 2 x + x + y = y − x + y + xy = x + y, 22, 2 x + xy = y + x − y x + y − xy = x, 23, 3 xy − = y x ( x + y + ) + y + y = 6, 9, ( x + y )( y + x ) + x + y = 12 x + y + xy + = y, 24, 2 x + y + xy + = x x + xy + y + x + y = 9, 10, 2 3 x − xy − y − x − y + = x − xy + y = x − y, 25, 2 x + xy + y = 3x + y x − xy + y + x = 1, 11, xy − y + y = x + xy − y + x − y = 0, 26, 2 3 x + y = 10 2 x − xy + x = 1, 12, 2 x + xy − y + y = x − xy + y = x − y + 2, 27, 2 2 x − xy + y = x − y + x + xy + y − x = 0, 13, 7 xy − y − y + = x + y + y = x + xy, 28, 2 2 x + y + xy = 1 + x + y + y = x + xy, 29, 2 x + y = x + y + xy x + = xy + ( y − x ) , 30, 2 x + y + xy = y − x − xy + y + x = 3, 6, 2 x − xy + y − y = −3 x − xy + y + x + = 0, 7, xy + y − y = 4 x + x − y + = 0, 14, 2 4 x − xy + y = x + x − y + = 0, 15, 2 x + y + xy = y CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN TĂNG THIẾT GIÁP Bài Giải hệ phương trình sau tập hợp số thực x − xy + y = x3 + y , 1, 2 x − xy + y = x y + = xy , 17, 2 x + x y + xy = 3x + y x + y = x − y − xy, 2, 2 2 x + y − xy = x + y + xy ( x + y ) = 4, 18, ( x + y )( xy + 1) = 2 x − y = x − y, 3, 2 x + y = x + y + xy + 2 x + y + 3xy ( x + y ) + x + y = 12, 19, ( xy + 1)( x + y ) = x + y + x + y = 4, 20, 3 xy = x − xy + y = x + y, 4, 2 x − xy + y = x + y + x + xy + = y + x, 5, 2 x + y = x − y − xy ( x − y ) + x − y = 6, 21, ( x − y )( xy − 1) = y + y x + 3x − y = 0, 6, x + xy = x + y + x y = 3, 22, 2 x y + xy + x + y = 4 x y − xy − y = −9, 7, 2 6 x y = y + x 2 x − y + x y + xy = 2, 23, 2 x y − xy + x − y = ( x + y )( x + y + ) = 3, 8, ( x + y )( x + y + ) = x + y + xy + x + y = 7, 24, xy + y + x + y = ( x + y )( x + y + 1) = 2, 9, y = x + x + ( x − y )( x − y + 3) = 4, 25, ( x + y )( x − y + 1) = 5 x y − xy + y − ( x + y ) = 0, 10, 2 xy ( x + y ) + = ( x + y ) x + xy = y + 1, 26, x + xy + y = x + y + y = 8, 11, x ( x + y ) = 4 x ( x + y ) = y + y + 1, 27, 2 x + y = x + y + ( x − 3) = 0, 12, y ( x + y ) = x ( x + y ) + ( y − y − 3) = 0, 28, 2 x + y + x + y + xy = x − y = y + 1, 13, x ( x − y ) = ( y − 1)( y + ) = x ( x − ) , 29, ( y − )( y + ) = x ( x − ) x − y + xy + xy = 2, 14, 2 xy − xy + x y + y = ( x − 1)( x − 3) + y ( − y ) = 0, 30, ( x − )( x − ) + ( y + 1)( − y ) = x − y + xy + x y = 3, 15, 2 y + xy + x y = y ( y − x ) = ( x − 1)( x − 3) , 31, y ( y − x ) = ( x − )( x − ) x ( x + y − 1) − = 0, 16, ( x + y ) − + = x CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM x = ( y − 1)( y − ) + x, 32, y + = ( x − 1)( x − ) + y TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN TĂNG THIẾT GIÁP Bài Giải hệ phương trình sau tập hợp số thực 6 xy + y + = x + y , 1, 2 5 xy + x + = y + x xy + x + = y , 18, 2 x y + xy + = y x + y + x y + xy + xy = − , 19, x + y + xy (1 + x ) = − 4 2 x + x y + x y = x + 9, 20, x + xy = x + ( x + y )( x + y ) = y + 1, 2, ( x + y )( 3x + y ) = x − x + ( x + 1) = xy + y, 3, 2 x + y = x + y ( x + ) = ( y + 1) , 4, 2 y + 3x ( y + 1) = ( y + ) x + 12 y = xy + 9, 5, y + 13 x = xy + 10 ( x − 1)( y − 1)( x + y − ) = 6, 21, 2 x − y − x − y − = 8 x y + 27 = 18 y , 22, 2 4 x y + x = y x + = y + y + xy, 6, y + = x + x + xy x + 12 y = y + xy + 9, 7, 2 y + 12 x = + x x + y = x + y, 8, 7 + xy = x + 10 y 1 + x y = x , 23, 1 + y + xy = x 5 xy = x + x + y + 1, 24, 3 xy + y = x + + y 6 xy = y + x + y + 1, 25, 1 + x + y = xy + x y ( x + y + 1) = x, 26, 2 y ( y + xy − x ) = x 6 xy = + x + y , 27, 2 x + y + x + y = xy x − xy + y = x + y − 3, 9, y − xy = x − y + x + xy = 4, 10, xy + y = x + y + y + xy = x, 11, x − xy + x + = y 5 xy + y = x + 1, 28, 2 x + y + x − y = xy x y + xy = 2, 29, 2 ( x + y ) ( x y + xy + 1) = ( x + y ) ( x + y ) = 4, 30, 2 ( x − y ) ( x + y ) = xy + y + x = y, 31, x + xy = y 4 ( x − y ) − = 12 y, 12, 2 5 ( x + y ) − 10 = 12 x x + y + ( xy + 3x + y ) = 16, 13, 2 x − y + ( xy − x − y ) = −9 3 x + y + x + y = 4, 14, xy + x + y = x + y + xy = 3, 15, x − y + xy = x + x y + y = 5, 16, 2 x + y = x + x y + y = 4, 17, x + y = CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM x + x y + xy + y = 0, 32, x + y = y x −1 + = 2, x −1 33, y x + xy = TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN TĂNG THIẾT GIÁP Bài Giải hệ phương trình sau tập hợp số thực x + y + xy = 0, 1, 3 3 x + y + x y = 12 x + = x ( y − 1) , 17, y − = y ( x − 1) x y − = , 2, y x x + y = 13 x − y − x + y = −3, 18, y − xy + x = −4 6 x − xy − 12 y = 0, 3, 17 x + y = 16 x − xy + y + 15 = 0, 19, 2 x − xy + y + = x3 + = ( x − x + y ) , 20, y +1 = ( y − y + x) ( x − y ) xy = 30, 4, ( x + y ) xy = 120 y + y = x + x, 21, 2 y = x − 3 , 3 x − y = x+ y 22, x + y = ( x + 1)( y + 1) + x − y = 6, 5, ( x − 1)( y + ) + x + y = x3 y + = y , 6, x x y + y = x + xy = y , 7, 2 x + y + xy = x + y = 2, 23, ( x + y )(1 + xy ) = 32 3 x = x + y , 8, 2 3 y = y + x 1 + xy = x + 1, 9, 2 x + y = xy − 3x − y = 16, 10, 2 x + y − x − y = 33 x + y = 5, 24, ( x + y )( + xy ) = 2187 2 x + y = 1, 25, ( x + y )( xy + 1) = 32 x + y = 4, 26, 5 8 x + x = y + y 3x − y − x − y = 3, 11, 2 x + y − 3x + y = x3 = x + y, 12, y = y + x x + y + ( x + y ) = 6, 13, ( y + 1) + ( y + 1)( x + 1) = ( x + 1) x + x = y + y, 14, 2 x + y = x + y + x + xy − y = x − y, 27, x + xy = x − x = y − y , 28, 2 x − xy − = x − x = y − y , 29, y = x + x − = y − , x y 30, x = y + x + xy + 12 y = 0, 15, 2 x + y = 12 4 x + y ( x − 1) = 7, 16, 3 y + x ( y − 1) = CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM x + y + x + y = 8, 31, 2 x − y + xy − x + y − = TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN TĂNG THIẾT GIÁP Bài Giải hệ phương trình sau tập hợp số thực 1 x y y + x − xy = x + y − 1, 11, 2 x + y = x − xy + y y +1 x +1 xy 2 = 7, xy + x + y + ( x + y) 1, x + = x+ y 2 = (10 − xy ) , 3 ( x + y ) + ( x − y) 2, 2 x + = x− y 85 2 = , 4 xy + ( x + y ) + ( x + y) 3, 2 x + = 13 x+ y 2 = 85, 12 xy + 12 x + 12 y + ( x + y) 4, 6 x x + y + = 13 x + y ) ( ) ( 2 = 13, 8 ( x + y ) + xy + ( x + y) 5, x + = x+ y x 2 x + = , y +1 6, y y + = x +1 2 x = y + x , 12, 2 y = x + y 2 x + y = x , 13, 2 y + x = 32 y x3 − x + x + = y, 14, y − y + y + = x 1 y − = xy − xy , 15, 2+ = ( x + 1) ( x + ) xy − x = 2, 16 16, = + ( x + 1) ( y + 1) x + xy = 1, 17, x xy 1− x = 1+ 1− x ) ( ) ( x − 16 y − = , y 18, x x − xy + y = 1 + = 2, 3 19, ( x + y + 1) ( x − y + 1) 2 x + 2x = y = 3, 2 x + 2 x +y 7, 2 y 1 + = x2 + y2 2 = 7, 4 ( xy + x + y ) + ( x + y) 8, x + = x+ y 17 3x 2x − y +1 + x + y = , 9, x + xy = − 15 2x − y +1 x y = y + 4, 10, 2 y x = x + CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM y ( x + 1) = x − x , 20, y ( x − y ) = x2 − x2 2y x + y − + x = 1, 21, x + y + y = 22 x TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN TĂNG THIẾT GIÁP Bài Giải hệ phương trình sau tập hợp số thực x x 3 + = 12, 1, y y 2 x y + xy = x + y = xy + y, 17, 2 x + 3xy = y + x x + y − x + y = 1, 18, 2 3 x − y − x − y = x − xy + x + y = 0, 2, 2 x − x y + x + y = x y = 16, 3, 3 x + y = 2 x − x ( y − 1) + y = y, 19, 2 x + xy − y = x − y x − xy + x + y = 0, 20, 2 x − x y + x + y = 27 x y + 125 = y , 4, 2 45 x y + 75 x = y x + y = 6, 21, y + ( x − 3) y − 48 y − 48 x + 155 = x + y = 2, 5, 2 x − 2x + 2x = y x − x = ( xy + y + )( x + ) , 22, 2 x + x − = y ( x + 1) x + xy − x − y + = 0, 6, 3x + xy − x + y = ( x + y + 1)( x + y + 1) = 12, 23, x + y + ( x + 1)( y + 1) = 11 y + xy = 8, 24, x y − y = x2 + y3 = y , 25, x + y = y x + y + xy = xy + 7, 26, − x y + xy + xy + 11( x − y ) = 28 x + y + x + y = 4, 7, 2 2 x + xy − y − x + y + = 2 x + xy + y + x + y + = 0, 8, 2 x + xy + y + 12 x + 12 y + 10 = 2 x + xy + y + x + y − = 0, 9, 2 3 x − 32 y + = x − y = 3x + 1, 10, 2 x + y = x + ( x + 1) ( x + y ) + x ( x + 1) = − y, 11, x ( x + 1) = − y x + xy + y + x = 0, 12, xy + y + y + = x + y = ( x + y ) + x y + x + 4, 13, 2 3 x + y + y + = x 6 x y + y + 35 = 0, 14, 2 5 x + y + xy + x + 13 y = x + y = xy + x + y, 15, 2 x − y = x3 − y = ( x − y ) , 27, 2 x + y = x + y + x − x = y − y, 28, x + y = x + y = xy , 29, 2 x + y = xy + xy − y − x + = 0, 30, 2 x − y − x − y + 22 = 2 x y − y = −1, 31, 2 xy − y = −2 3x − y x + x + y = 3, 16, y − x + y = x2 + y2 CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM x y x y x y + − + + + = −2, 32, y x y x y x 2 x + y − x + = TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN TĂNG THIẾT GIÁP Bài Giải hệ phương trình sau tập hợp số thực x − xy + y = 1, 1, 4 x + y = x + y x + x + y − y = 2, 17, 2 x y + x + y = 23 2 x + 3xy = y − 13, 2, 3 y + xy = x + 11 x (1 − y ) = y ( x + y ) , 3, 2 2 x + xy − y = x ( x − y )2 + y = 3, 18, 2 x + xy − y − x + 13 y = x − xy + x + y = 0, 19, 2 x − x y + x + y = y ( xy − ) = 3x , 4, 2 y + x y + x = 9 y ( x − 1) = −125, 20, 2 45 x y + 75 x = y y ( x + y )2 = 9, 21, 3 x − y = x − xy + y = 0, 22, x + xy + x = 27 x3 + y = 2, 5, + xy 3x + y + xy = x + x + y = 7, 6, xy − x + y = x + y = x − y, 7, 3 y − x = y − x ( x + x + 1)( y + y + 1) = 3, 8, (1 − x )(1 − y ) = 2 y x + x + y − y − = y , 9, 2 y + xy + = y x − xy − x + = y − xy − x , 10, 2 y − yx + y − = y + xy − x x y − y + x = 0, 11, 2 y x + y + x = 2 xy + y − x y = x + y, 12, 2 xy ( x + y ) − = 3xy − ( x + y ) 16 x y − y = ( xy − y ) ( xy + 3) , 13, 2 2 4 x y − xy + y = ( x − 1) ( y + ) = y ( x + 1) , 14, 2 ( y − 1) ( x + ) = x ( y + 1) x + y ( x − 1) = 60, 15, 3 y + x ( y − 1) = 48 y + x + xy + = 6, y 16, x y − y + x y + x = CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM xy + = 3x + y, 23, 2 x − x + y = y − x + xy + y = y − 1, 24, 2 x + x y = x − x + x + x + y = 9, 25, 2 3x + x y + xy + x = 18 x − y − 15 y − 14 = ( y − x ) , 26, xy + 11x + y + 13 = 21 y = x + 20, 27, x ( y + 20 ) = 21 x y + xy + x − y = 0, 28, xy + y − y + = x + xy + y + x = 0, 29, xy + y + y + = x + y + x − y = 2, 30, 2 x y + x + y = 23 x y + ( x + y ) = 8, 31, xy + = 6 − x − y xy = x + y + 1, 32, 2 x y = 10 y − TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN TĂNG THIẾT GIÁP Bài Giải hệ phương trình sau tập hợp số thực x + xy + y = 3, 17, x + xy − x − y + = x + y + y = 4, 1, ( x + xy ) ( y + 1) + x = x + x + y − y = 2, 18, 2 x y + x + y = 23 x y − x + y = 1, 2, 2 2 x + y = x + x ( y + 1) = y − 2, 19, 2 2 1 + x y + x y + y ( x + 1) = 12 y 8 x − xy = y − x , 3, x − x y = y x y (1 + y ) + x y ( y + ) + xy = 30, 20, 2 x y + x (1 + y + y ) + y = 11 x + xy + x + y = 16, 4, ( x + y )( + xy ) = 32 x + xy = x + y, 21, 2 x − ( x + y − 1) x + y + xy = x ( y + 55 ) = 64, 5, xy ( y + y + 3) = 12 + 51x y ( x + ) = 8, 6, y ( x + 3x + x − 1) = 2 x y + x + x = 2, 7, 2 2 x y − x y + xy = x + y + x + y = 8, 8, xy ( xy + x + xy + 1) = 12 2 x + y = + x + y, 9, 3 xy = y + x + y + x + xy + y = x + 10 y, 10, 2 2 x + xy + y = y x + xy + y = x + y + 6, 11, 2 x + xy + y − 3x − 12 y + 16 = x + y + xy − 18 x − 22 y + 31 = 0, 12, 2 2 x + y + xy + x − 46 y + 175 = x − y = 240, 13, 3 2 x − y = 3( x − y ) − ( x − y ) x + y − x = − + 3, 22, y + x − y = − − 3 x − xy + = 0, 23, 2 x + y + x + y + = xy − = − y , 24, xy = + x x ( y + 1)( x + y + 1) = 3x − x + 1, 25, xy + y + = x y = ( x + )( − x ) , 26, 2 y − x − xy + 16 x − y + 16 = x + y − x + xy = 0, 27, xy ( x + y ) + ( x − 1) = y (1 − y ) x + y + x + y + = 0, 28, x + xy + y + x + = x + y + xy + = y, 29, 2 y ( x + y ) = x + y + x + x y + y = y x + x y + x, 14, 3 x ( y − x ) = 1 + x y = 19 x , 30, 2 xy + y + x = x − x = y + 11 y, 15, 2 ( x − y ) = 27 ( x − 1) + ( x − 1) y + y = 20, 16, 2 x + ( y + 1) = CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM ( xy + 1)3 = y ( − xy ) , 31, xy ( y − 1) = y + x y + xy − = y, 32, x y − x + xy = TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN TĂNG THIẾT GIÁP Bài Giải hệ phương trình sau tập hợp số thực x − x y + x y = 1, 1, x y − x + xy = x − y = 35, 17, 2 x + y = x − y 3 ( x − y ) = xy, 2, 2 x y = x + y = 9, 18, 2 x + y = x + y x + y = 91, 19, 2 4 x + y = 16 x + y x + y = 2, 3, 2 x y + xy + y = x y − x + y = 0, 20, x + x + y − 12 x + 13 = x + y = 6, 4, 2 x y + x = 4 x + xy = y , 21, y + x y = x y + xy = x + y 5, 7 y + = x + x y + y + 3x − y = 0, 6, x + xy = y ( x2 + x + 2) = x ( y2 + 6) , 22, 2 ( y − 1) ( x + x + ) = ( x + 1) ( y + 1) x + xy + = x + y, 7, 2 x + y = x + 3xy = −49, 23, 2 x − xy + y = y − 17 x x + y + + xy = y, 8, y x + y − = + x2 1 2 x + 2y = 2( x + y ), 9, − = y2 − x2 x 2y 5 x + y + = 0, 24, 57 = − y ( 3x + 1) 4 x + 3x − 25 x + y = 2, 25, 2 x + xy + y = y ( x + 1) y + = xy ( y − 1) , 26, 2 xy ( xy − ) = xy ( x + y ) + x y − x + y = 0, 10, 2 x − x + y + 10 = x ( x − y ) + 1 = y ( y − xy + ) , 27, 3 x + y + = y ( x + ) x3 + y = 1, + xy 28, 2 12 ( y − ) + 15 = x y ( y + 3) − x y + y = x, 11, x − x + + y = ( x − x + )( y − y + ) = 18, 12, 2 x + y + xy − x − y + 14 = 4 xy − y + x = 0, 13, 2 y + x y + 20 = x3 + y = x − y, 29, 2 x − y = 81( x + y ) = 698, 14, 2 x + y + xy − x − y + = xy − x + y = 3, 15, 3 x + 12 x + x = − y + y + x2 y2 + y4 + x2 = y , 30, 2 xy + y = x + xy x + xy = x + y + 2, 31, 4 2 x + y + x y = x = xy + y 32, 3 y = xy + x y = − x + 3x + y, 16, x = −2 y − y − CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN TĂNG THIẾT GIÁP Bài 10 Giải hệ phương trình sau tập hợp số thực x − y ( x + y ) + = 0, 1, ( x + 1) ( x + y − ) + y = x y + xy + x + y + xy = 11, 18, 2 3 x y − xy + x − y + xy = 17 x y − xy + y = 1, 2, 2 x + = x − y x − y − xy = −4, 19, 2 2 xy + y − x y − y = ( x − y ) + x + y = y , 3, 2 x − x y + 3x = − y x + x y + xy + y = 2, 20, 2 2 x + x − x y + y + y = −2 x3 y + x y + y x = x + x − y , 4, 2 x + x + y = 12 x − 13 ( x + x ) y − y + y + = 0, 21, 2 3 xy + x y + = ( − x ) y x − xy − xy + y = 0, 5, 16 x + x − y + = 5 x ( y + 1) = ( x + y ) , 22, 2 5 y ( x − 1) = x + y x + y + x + y = 4, 6, xy ( xy + x + y + ) = 5 y ( xy − 1) = ( y + 1) 23, x ( xy − 1) = x + y + x = 3x + 4, 7, x + y + = y x + y = 1, 24, 2 x − xy + y + y = x + xy − x + y = 0, 8, 2 x + x y − x + y = y (1 + x y ) = 3x , 25, 6 1 + x y = x 2 x − xy − y = 2, 9, 2 2 x − 3x − xy − y + = ( x − 1)( y − 1) = xy , 26, 2 x + y + xy − x − y + 14 = x + x ( y − ) + x ( y − 1) − y + = 0, 10, 2 x + y + xy − y + = x + y = 1, 27, 9 x + y = 2 x + x ( y + ) + y ( y − 1) − y ( x + 1) + x = 0, 11, 2 x y − x + y + y − = y + y x + 3x − y = 0, 28, x + xy = x + x ( y − ) + x − x + y = 0, 12, 2 2 x − y − x + y = 6 x − y + xy − x − 12 y = 0, 29, x − xy + = xy ( xy + y + 1) + y + = y , 13, xy + x + = y ( x − 1) = y ( − y ) , 30, ( y − 1) = ( − x ) ( x − x + 1) x + x y − 3x + y + xy + x − y = 3, 14, 2 2 x − y − y = x − y + = 0, 31, 2 x + y + x = y x − xy + y − x + = 0, 15, 2 2 x + y + x y = xy + xy − x + y + = 0, 16, 2 x y = y + xy + x y + xy + xy − y + = y , 32, 3 xy − y + = y x + y + x = 3, 33, 2 xy x − y + x + y − = −1 ( x + 1) + y + y = 7, 17, 2 y ( y + x ) = y + 2 CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM 10 TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN TĂNG THIẾT GIÁP Bài 11 Giải hệ phương trình sau tập hợp số thực x + y = ( x + 1)( y + ) , 1, xy = x + xy + x y − y = 2, 16, 2 x y + x + y = 1 x − y + x − y = , 2, x + y − + = 25 x y 12 x − 12 y + x + 10 xy + y = 4, 17, 2 x + y = xy ( y + x ) = 2, 18, 3 x + y + x + y = 10 x y + x + y = 15, 3, 2 x + y = x + y + ( x + 1) y + = xy ( y − 1) , 19, 4 xy ( xy − ) = xy ( x + y ) + x + y = 1, 4, 3 x − y − x y = y ( xy − 1) x − xy + x y − x = 1, 20, 2 x y + xy − y = x − 3x + 22 − x = y + y − y, 5, 2 x + y − x + y = x ( x + ) + y ( y + x + 1) = 3, 21, y ( x + ) + x = x3 − 3x + = y + y , 6, 2 x + y + x − y = x + xy + x − y = 4, 22, 2 x + xy + y + y = x + xy + 42 = 0, 7, 2 2 x − xy − y + x + 10 y = 35 x y − 54 x + y = 0, 23, x + y = 12 x − 45 x y + xy + x − y = 0, 8, 2 xy + y − y + = x3 + = x + y, 24, 2 6 y + ( x + y ) = y+ = 2, 2x + y 9, 5 x + xy = + (2x + y ) x + xy + x + y = 10, 25, 2 x + y = 3 x + y + xy = 3x + y, 26, 2 x y = x + y − 2 xy ( x + y ) = x + , 27, x x + y = 2 x ( x + 1)( y + 1) + xy = −6, 10, 2 y ( x + 1)( y + 1) + xy = x ( x − 1) + ( xy + 3) y = x + y 2, 11, y ( y + 1) + ( xy + 3) x = ( x − y )2 = − x y , 28, x ( xy + y + 1) = y ( xy + 1) + 3 xy ( x + y ) = + x + y , 12, 3 3 2 9 x y − xy ( x + y ) + x y = 2 y + xy = y − x − 1, 29, 2 y + x y = y − x x + y + xy ( x − x − y ) = −2, 13, 2 2 ( x − y ) − xy ( x − y + 1) = x + xy − x − y = 0, 30, 2 x − ( x + y − 1) x + y + xy = x + xy = −4 y , 14, 4 x + y = 3 x ( y − 1) − y ( x + 1) + xy + = x + y, 31, 2 y ( x + ) = 8 x − y = 63, 15, 2 y + x + y − x = CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM 11 TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN TĂNG THIẾT GIÁP Bài 12 Giải hệ phương trình sau tập hợp số thực x y + xy = 2, 1, 3 x y + x + y x + y = x3 − y = x − y, 16, 2 3 x + y = ( x + y ) ( x + y ) x y + x y − x = 6, 2, 2 x y + xy + x + x = x − xy + y = x + y, 17, 2 x + xy + y = x + y − x 3 + xy + = y , 3, x ( xy + ) + x = y + x 3 xy + x = x + y + 2, 18, xy + y − x = + y y ( x + y + 1) = x + x, 19, x ( x − y + 1) = y − y 3 x − x − 36 x = y − 26 y − 72 y + 308, 4, 3 3 x − 12 x = 15 y + 23 y + 178 4 x + y − + y = x , 20, 4 2 2 x + y − x − y = x y − 10 xy − x y + 3x − x + = 0, 5, 2 x y − x + y = ( x + y ) x y = 2, 21, 3 2 ( x + y ) ( x y + x y − 3xy + ) = 8 x + x = y + y , 6, 2 x − x + = y − y 3 x − x ( y + 1) + y = 0, 22, 2 x − x ( x − 1) + y = 10 y xy + y + = 1, 7, x + y xy + y + 16 = ( x + y ) x + y = 1, 23, 2 21x + y + 48 x − 48 y + 28 xy = 69 ( x − x + x )( y − y + y ) = 16 y , 8, 2 2 x y − xy + y + y = 10 y xy = y + x , 24, 2 y x + y = x x + y + x + y = 0, 9, 2 x − y + xy − x + y − = x + y = 1, 25, 21x + y + 96 x + 28 xy = 117 ( x − 1)( y − 1) = 11xy, 10, 2 x + y + xy − x − y + 14 = x − y + y + x − y + = 0, 26, x + y = x + y + xy + x + y = 10 27, 2 x + y + xy + 3x + y = 21 14 x − 21 y + 22 x − 39 y = 0, 11, 2 35 x + 28 y + 111x − 10 y = x y = xy (1 + x ) + 2, 28, 2 xy = x y + xy + xy ( x + y ) = y − x, 12, y + xy + = y x = x y + xy − 1, 29, y = + xy 4 x + y + x + y = 7, 13, 2 4 ( x − y )( 25 + xy ) = 105 + 16 x + 68 y x + yx + y = 3, 30, x y + x y = 2 1 ( x + 1) ( y + 1) + xy = 0, 14, ( x + 1)( y + 1) + 10 xy = x − y = 1215, 31, 3 2 2 x − y = x − y − 18 ( x − y ) ( xy + 1)3 + x ( y − 1) = x − 1, 15, x + = xy + CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM x + y = xy + 32, 2 x + y = xy + 12 TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN TĂNG THIẾT GIÁP ... HOÀNG MINH THI; XYZ1431988@GMAIL.COM x = ( y − 1)( y − ) + x, 32, y + = ( x − 1)( x − ) + y TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN TĂNG THI? ??T GIÁP Bài Giải hệ phương trình sau tập hợp số... BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM x + y + x + y = 8, 31, 2 x − y + xy − x + y − = TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN TĂNG THI? ??T GIÁP Bài Giải hệ phương trình sau tập hợp số thực... x = −2 y − y − CREATED BY HOÀNG MINH THI; XYZ1431988@GMAIL.COM TRUNG ĐOÀN – SƯ ĐOÀN – QUÂN ĐOÀN TĂNG THI? ??T GIÁP Bài 10 Giải hệ phương trình sau tập hợp số thực x − y ( x + y ) + = 0,
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