Question

Решите систему уравнений методом подстановки: 50 Б

1) x = 3.5 y
4х - 3y = 22

2) 5х - 4у = 8
х - у = 2

И методом сложения
1) 5х + 3у - 1.4
-7х - 10у = 5

Answer 1

$1) \left \{ {{x=3,5y} \atop {4x-3y=22}} \right. \\ 4*3.5y-3y=22\\ 14y-3y=22\\ 11y=22\\ y=22:11\\ y=2\\ x=3.5*2=7$
ответ: (7; 2)

$2) \left \{ {{5x-4y=8} \atop {x-y=2}} \right. \ \ \ \left \{ {{5x-4y=8} \atop {x=2+y}} \right. \ \ \ \\ 5(2+y)-4y=8\\ 10+5y-4y=8\\ 10+y=8\\ y=8-10\\ y=-2\\ x=2+(-2)=2-2=0$
ответ: (0; -2)

$3) \left \{ {{5x+3y=1.4 \ |*10} \atop {-7x-10y=5 \ |*3}} \right. \ \ \ \left \{ {{50x+30y=14 } \atop {-21x-30y=15}} \right. \ \ \ \\ 50x-21x+30y-30y=14+15\\ 29x=29\\ x=29:29\\ x=1\\ 5*1+3y=1.4\\ 5+3y=1.4\\ 3y=1.4-5\\ 3y=-3.6\\ y=-3.6:3\\ y=-1.2$
ответ: (1; -1,2)