Question

{4(x-2)+2(7-4x)=20+2(y-3)
{5(2y+3)+2(6x-y)=3(5x-3)+31
РОЗВЯЖІТЬ систему рівнянь будь ласка
Дякую

Answer 1

Ответ: x=-2 1/19 ; y=2/19

$\left \{ {{4(x - 2) + 2(7 - 4x) = 20 + 2(y - 3)} \atop {5(2y + 3) + 2(6x - y) = 3(5x - 3) + 31}} \right. \\ \\ \left \{ {{4x - 8 + 14 - 8x = 20 + 2y - 6} \atop {10y + 15 + 12x - 2y = 15x - 9 + 31}} \right. \\ \\ \left \{ {{4x - 8x - 2y = 20 - 6 + 8 - 14} \atop {10y + 12x - 2y - 15x = - 9 + 31 - 15}} \right. \\ \\ \left \{ {{ - 4x - 2y = 8 \: \:| \times 4 } \atop { - 3x + 8y = 7 \: \: \: \: \: \: \: \: \: \: }} \right.$

$\left \{ {{ - 16x - 8y = 32} \atop { - 3x + 8y = 7}} \right. + \\ - 19x = 39 \\ x = - \frac{39}{19} = - 2 \frac{1}{19}$

И вместо х поставим -2 1/19

$- 3x + 8y = 7 \\ - 3 \times ( - \frac{39}{19} ) + 8y = 7 \\ \frac{117}{19} + 8y = 7 \\ 8y = 7 - \frac{117}{19} = 7 - 6 \frac{3}{19} = 6 \frac{19}{19} - 6 \frac{3}{19} = \frac{16}{19} \\ y = \frac{16}{19} \div 8 = \frac{16}{19} \times \frac{1}{8} = \frac{2}{19}$