Question

Розв'язати систему способом підстановки:

1) $\left \{ {{2x+3y=6} \atop {x+7y=-6}} \right.$

2) $\left \{ {5x+2y=15} \atop {8x+3y=20}} \right.$

Answer 1

1)

$2x + 3y = 6 \\ x + 7y = - 6 \\ \\2( - 6 - 7y) + 3y = 6 \\ x = - 6 - 7y \\ \\ - 12 - 14y + 3y = 6 \\ - 11y = 6 + 12 \\ - 11y = 18 \\ y = - \frac{18}{11} \\ y = - 1 \frac{7}{11 } \\ \\ x = - 6 - 7 \times ( - \frac{18}{11} ) = - 6 + \frac{126}{11} = \\ - 6+ 11 \frac{5}{11} = 5 \frac{5}{11}$

Ответ: ( 5 5/11 ; - 1 7/11 )

2)

$5x + 2y = 15 \\ 8x + 3y = 20 \\ \\ 2y = 15 - 5x \\ 8x + 3y = 20 \\ \\ y = 7.5 - 2.5x \\ 8x + 3(7.5 - 2.5x) = 20 \\ \\ 8x + 22.5 - 7.5x = 20 \\ 0.5x = 20 - 22.5 \\ 0.5x = - 2.5 \\ x = - 2.5 \div 0.5 \\ x = - 5 \\ \\ y = 7.5 - 2.5 \times ( - 5) = \\ 7.5 + 12.5= 20$

Ответ: ( - 5 ; 20 )