1. Умножим второе уравнение на 2:
4x+2y=9 |*2 ⇒ 8x+4y=18
и сравним с первым: 8x+4y=7
Т.е. одно и то же выражение должно одновременно равняться и 7, и 18. Это невозможно, значит, данная система несовместна, т.е. не имеет решений. Либо у вас ошибка в условии.
2. Умножаем первое уравнение на 2 и вычитаем из него второе:
Проверяем:
2*(-3) - 4*(-5) = -6+20=14
4*(-3) + 3*(-5) = -12-15 = -27
3.
![\left\{\begin{array}{c}{-x+2y+z=7}\\{2x-y+6z=19}\\{-4x+3y-z=8}\end{array} \ \textless \ =\ \textgreater \ \left\{\begin{array}{c}{-x+2y+z=7}\\{3y+8z=33}\\{5y+5z=20}\end{array} \ \textless \ =\ \textgreater \](https://tex.z-dn.net/?f=++%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bc%7D%7B-x%2B2y%2Bz%3D7%7D%5C%5C%7B2x-y%2B6z%3D19%7D%5C%5C%7B-4x%2B3y-z%3D8%7D%5Cend%7Barray%7D+%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C++++%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bc%7D%7B-x%2B2y%2Bz%3D7%7D%5C%5C%7B3y%2B8z%3D33%7D%5C%5C%7B5y%2B5z%3D20%7D%5Cend%7Barray%7D+%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C++ "\left\{\begin{array}{c}{-x+2y+z=7}\\{2x-y+6z=19}\\{-4x+3y-z=8}\end{array} \ \textless \ =\ \textgreater \ \left\{\begin{array}{c}{-x+2y+z=7}\\{3y+8z=33}\\{5y+5z=20}\end{array} \ \textless \ =\ \textgreater \")
![\left\{\begin{array}{c}{-x+2y+z=7}\\{3y+8z=33}\\{y+z=4}\end{array} \ \textless \ =\ \textgreater \ \left\{\begin{array}{c}{-x+2y+z=7}\\{5z=21}\\{y+z=4}\end{array}\ \textless \ =\ \textgreater \](https://tex.z-dn.net/?f=++%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bc%7D%7B-x%2B2y%2Bz%3D7%7D%5C%5C%7B3y%2B8z%3D33%7D%5C%5C%7By%2Bz%3D4%7D%5Cend%7Barray%7D+%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C+++%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bc%7D%7B-x%2B2y%2Bz%3D7%7D%5C%5C%7B5z%3D21%7D%5C%5C%7By%2Bz%3D4%7D%5Cend%7Barray%7D%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C++ "\left\{\begin{array}{c}{-x+2y+z=7}\\{3y+8z=33}\\{y+z=4}\end{array} \ \textless \ =\ \textgreater \ \left\{\begin{array}{c}{-x+2y+z=7}\\{5z=21}\\{y+z=4}\end{array}\ \textless \ =\ \textgreater \")
![\left\{\begin{array}{c}{-x+2y+z=7}\\{z=4,2}\\{y+z=4}\end{array} \ \textless \ =\ \textgreater \ \left\{\begin{array}{c}{-x+2y+z=7}\\{z=4,2}\\{y=-0,2}\end{array}\ \textless \ =\ \textgreater \](https://tex.z-dn.net/?f=++%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bc%7D%7B-x%2B2y%2Bz%3D7%7D%5C%5C%7Bz%3D4%2C2%7D%5C%5C%7By%2Bz%3D4%7D%5Cend%7Barray%7D+%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C+++%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bc%7D%7B-x%2B2y%2Bz%3D7%7D%5C%5C%7Bz%3D4%2C2%7D%5C%5C%7By%3D-0%2C2%7D%5Cend%7Barray%7D%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C+ "\left\{\begin{array}{c}{-x+2y+z=7}\\{z=4,2}\\{y+z=4}\end{array} \ \textless \ =\ \textgreater \ \left\{\begin{array}{c}{-x+2y+z=7}\\{z=4,2}\\{y=-0,2}\end{array}\ \textless \ =\ \textgreater \")
![\left\{\begin{array}{c}{-x+2*(-0,2)+4,2=7}\\{z=4,2}\\{y=-0,2}\end{array} \ \textless \ =\ \textgreater \ \left\{\begin{array}{c}{-x=2,8+0,4}\\{z=4,2}\\{y=-0,2}\end{array} \ \textless \ =\ \textgreater \](https://tex.z-dn.net/?f=++%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bc%7D%7B-x%2B2%2A%28-0%2C2%29%2B4%2C2%3D7%7D%5C%5C%7Bz%3D4%2C2%7D%5C%5C%7By%3D-0%2C2%7D%5Cend%7Barray%7D+%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C++++%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bc%7D%7B-x%3D2%2C8%2B0%2C4%7D%5C%5C%7Bz%3D4%2C2%7D%5C%5C%7By%3D-0%2C2%7D%5Cend%7Barray%7D+%5C+%5Ctextless+%5C+%3D%5C+%5Ctextgreater+%5C++ "\left\{\begin{array}{c}{-x+2*(-0,2)+4,2=7}\\{z=4,2}\\{y=-0,2}\end{array} \ \textless \ =\ \textgreater \ \left\{\begin{array}{c}{-x=2,8+0,4}\\{z=4,2}\\{y=-0,2}\end{array} \ \textless \ =\ \textgreater \")
Проверка:
-(-3,2) + 2*(-0,2) + 4,2 = 3,2 - 0,4 + 4,2 = 7 (+)
2*(-3,2) - (-0,2) + 6*4,2 = -6,4 + 0,2 + 25,2 = 19 (+)
-4*(-3,2) +3*(-0,2) - 4,2 = 12,8 - 0,6 - 4,2 = 8 (+)