Question

Решите систему:

{ y=x+z;

{ 7x+20y=150;

{ 35z-7x=-220;

Answer 1

{ y=x+z;
{ 7x+20y=150;
{ 35z-7x=-220

7x+20y+35z+(-7x)=150+(-220)
20y+35z=-70
20y=-70-35z
20y=-35(2+z)|÷20

y=-1,75(2+z)

у=x+z
x=y-z
x=-1,75(2+z)-z
x=-3,5-1,75z-z

x=-3,5-2,75z

35z-7x=-220
35z-7(-3,5-2,75z)=-220
35z+24,5+19,25z=-220
54,25z=-220-24,5
54,25z=-244,5|÷54,25
z=-4,5069

z=~-4,51


y=-1,75(2+z)
y=-1,75(2+(-4,51))
y=(-1,75)×(-2,51)
y=4,3925

y~4,39

x=-3,5-2,76z
x=-3,5-2,75×(-4,51)
x=-3,5+12,40258
x=8,9025

x~8,9

Проверка:

x+z=y
8,9+(-4,51)=4,39
4,39=4,39-истина.

7х+20у=150
7×8,9+20×4,39=150
62,3+87,85=150
150,15~150-истина

35z-7x=-2
35×(-4,51)-7×8,9=-220
-150,85-62,3=-220
-220,15~-220-истина.

Ответ: x~8,9; y~4,39; z~-4,51

Answer 2

Молодец)