Question

Розв'яжіть системи рівнянь

Answer 1

a) Ответ: x=123/337 ; 102/337

$[tex]\left \{ {{ \frac{x + 1}{3} - \frac{y - 2}{4} = \frac{2(x + 1)}{5} } \atop { \frac{x - 3}{4} - \frac{y - 3}{3} = 2y - x }} \right. \\ \\ \left \{ {{ \frac{4x + 4 - 3y + 6}{12} = \frac{2x + 2}{5} } \atop { \frac{3x - 9 - 4y + 12}{12} = 2y - x }} \right. \\ \\ \left \{ {{20x + 20 - 15y + 30 = 24x + 24} \atop {3x - 9 - 4y + 12 = 24y - 12x}} \right. \\ \\ \left \{ {{20x - 24x - 15y = 24 - 30} \atop {3x - 4y + 12x - 24y = - 12 + 9 }} \right.$

$\left \{ {{ - 4x - 15y = - 6 \: \: | \times 15 } \atop {15x - 28y = - 3 \: \: \ | \: \: \times 4}} \right. \\ \\ \left \{ {{ - 60x - 225y = - 90} \atop {60x - 112y = - 12}} \right. + \\ \\ - 337y = - 102 \\ y = \frac{102}{337}$

[/tex]

$И \: вместо \: у \: поставим \: 102/337 - 4x - 15y = - 6 \\ - 4x - 15 \times \frac{102}{337} = - 6 \\ - 4x - \frac{1530}{337} = - 6 \\ \frac{ - 1348x -1530 }{337} = - 6 \\ - 1348x - 1530 = - 2022 \\ - 1348x = - 492 \\ x = \frac{492}{1348} = \frac{123}{337}$

б) Ответ: x=-4 ; y=-6

$\left \{ {{ \frac{2.5x - 2y}{2} - 2x = 3 } \atop { \frac{3x - 2y}{3} + 4 = 3x}} \right. \\ \\ \left \{ {{ \frac{2.5x - 2y - 4x}{2} = 3 } \atop { \frac{3x - 2y + 12}{3} = 3x}} \right. \\ \\ \left \{ {{ - 1.5x - 2y = 6} \atop {3x - 2y + 12} = 9x} \right. \\ \\ \left \{ {{ - 1.5x - 2y = 6} \: \: | \times ( - 4)\atop { - 6x - 2y = - 12} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \right.$

$\left \{ {{6x + 8y = - 24} \atop { - 6x - 2y = - 12}} \right. + \\ 6y = - 36 \\ y = - 6$

И вместо у поставим -6

$- 6x - 2y = - 12 \\ - 6x - 2 \times ( - 6) = - 12 \\ - 6x + 12 = - 12 \\ - 6x = - 24 \\ x = 4$