Question

Решите системы уравнений a)Способ подстановки (x-y=-7 2x+y=10 Способ сложения 8x+13y=73 8x+24=2​

Answer 1

1)

$\displaystyle\bf\\\left \{ {{x - y = - 7} \atop {2x + y = 10 }} \right.\\ \displaystyle\bf\\\left \{ {{y = x + 7} \atop {2x + x + 7 = 10 }} \right. \\ \\ 3x = 10 - 7 \\ 3x = 3 \\ x = 3 \div 3 \\ x = 1 \\ \\ y = 1 + 7 = 8$

Ответ: ( 1 ; 8 )

2)

$\displaystyle\bf\\\left \{ {{8x + 13y = 73} \atop {8x + 24 = 2 \: \: | \times ( - 1) }} \right. \\ \displaystyle\bf\\ + \left \{ {{8x + 13y = 73} \atop { - 8x - 24 = - 2 }} \right. \\ \\ 13y - 24 = 73 - 2 \\ 13y = 71 + 24 \\ 13y = 95 \\ y = \frac{95}{13} \\ y = 7 \frac{4}{13} \\ \\ 8x + 13 \times \frac{95}{13} = 73 \\ 8x + 95 = 73 \\ 8x = 73 - 95 \\ 8x = - 22 \\ x = - 22 \div 8 \\ x = - 2.75$

Ответ: ( - 2,75 ; 7 4/13 )