Ejercicios de Sistemas de ecuaciones lineales 1 Hallar los valores de las incógnitas en las ecuaciones siguientes: x + 2y + 7z = –21 a) x – 2y + 6z = –14 7x + 6y – 3z = 17 b) 6x + 3y + 7z = –17 5x – y = 1 7x + y + 5z = –17 Solución: a) x = 2, y = –1, z = –3 c) x = –6, y = 4, z = –9 c) x + 7y + 4z = –14 2x – 9y – 5z = –3 8y + z = 23 b) x = 2, y = 9, z = –8 2 Resolver los siguientes sistemas de ecuaciones: x + 6y – 6z = 6 a) 8x + 8y + 3z = 41 5x + 3y + 9z = 39 b) Solución: a) x = 0, y = 4, z = 3 c) x = –1, y = 1, z = –2 x – 6y – 8z = 12 x – 4y – 9z = 21 8x – 6y – 5z = 45 x + 4y + 7z = –11 c) 3x + 5y + 3z = –4 7x – y + 7z = –22 b) x = 6, y = 3, z = –3 3 Hallar la solución de los siguientes sistemas de ecuaciones: x + 4y + 4z = –46 5x + 6z = –14 8x + 2y + 7z = –28 b) x – 2y + 7z = –26 x + y + 6z = –25 x + 2y + 2z = –10 c) 9x + 9y – z = 5 x – 6y – 3z = 17 8x + 6y + 7z = 44 7y + 5z = 45 d) 5x + 5y – 3z = –11 x + y – 6z = –13 e) x + 8y – 2z = 41 x+z=9 3x + y – 7z = –46 f) x + 5z = 0 y+z=2 3x – 3y + 5z = –6 a) Solución: a) x = 2, y = –8, z = –4 c) x = 5, y = –4, z = 4 e) x = 1, y = 7, z = 8 b) x = 0, y = –1, z = –4 d) x = –6, y = 5, z = 2 f) x = 0, y = 2, z = 0 4 Resolver: a) 6x – 6y – 7z = 10 4y – z = 18 x – y + 5z = 14 b) Solución: a) x = 9, y = 5, z = 2 c) x = –6, y = –5, z = 1 x – 2y + 8z = –31 y + z = –5 7x – 4y – 7z = 25 c) 6x – 7y + 3z = 2 x – 7y = 29 3x – y + 3z = –10 b) x = –1, y = –1, z = –4