2(Х+3у) +9=х+6 3(х-2у) =х+30 2X + 6Y + 9 = X + 6 3X - 6Y = X + 30 X + 6Y + 3 = 0 2X...

Question

2(Х+3у) +9=х+6
3(х-2у) =х+30

2X + 6Y + 9 = X + 6
3X - 6Y = X + 30

X + 6Y + 3 = 0
2X - 6Y - 30 = 0
_____________
+

3X - 27 = 0
3X = 27
X = 9

Подставим значение Х в одно из данных уравнений и найдем У:

X = 9
X + 6Y + 3 = 0

X = 9
X + 6Y + 3 = 0

9 + 6У + 3 =0
12 + 6У = 0
6У = -12
У = - 2

X = 9
У = -2

Ответ: (9; - 2)

ПРОВЕРКА:

2(Х+3у) +9=х+6

2(Х+3у) +9= 2(9 + 3*(-2)) + 9 = 2 ( 9 - 6) + 9 = 6 + 9
х+6 = 9 + 6

Answer 1

1)2(х+3у)+9=х+6
3(х-2у)=х+30
2x+6y+9=x+6
3x-6y=x+30
x+6y+3=0
2x-6y-30=0
3x-27=0
3x=27
x=9

9+6y+3=0
6y=-12
y=-2
(9;-2)

2) 5(3х+2)=7+12у
4(х+у)+х=31

15x+10=7+12y
4x+4y+x=31

15x-12y=-3
5x+4y=31 |*3

15x-12y=-3
15x+12y=93

30x=90
x=3

45+12y=93
12y=48
y=4

(3;4)

3)4(3х+у)-1=у-2х
2(4х-у)+19=-х

12x+4y-1=y-2x
8x-2y+19=-x

14x+3y=1 | *2
9x-2y+19=0 |*3

28x+6y=2
27x-6y=-57

55x=-55
x=-1

-14+3y=1
3y=15
y=5

(-1;5)


4) 2(х+2у)-7у=6
5(2х+у)-х=2у+60

2x+4y-7y=6
10x+5y-x=2y+60

2x-3y=6
9x+3y=60

11x=66
x=6
12-3y=6
-3y=-6
y=2
(6;2)