Question

Rozwiąż układ równań:
a)x+5/3-(1-y)=-3
y+5/2-(x-1)=4
b)x-1/4+2=y
y-3/3+5=x
c)x+5/2+2y-1/3=4
3x+1/2+5y+2/4=5
d)x+6/3+3y+1/2=5
y+1/2+x+5/8=2
e)x+2/2-y-2/4=3
x-2/2-3y+1/7=0
Na dziś.DZIĘKI!!!

Answer 1

. a)
x+5/3-(1-y)=-3 |*3
y+5/2-(x-1)=4 |*2

3x+5-3+3y=-9 |-2
2y+5-2x+2=8 |-7

3x+3y=-11 |*2
2y-2x=1 |*3

6x+6y=-22
6y-6x=3

12y=-19 |/12
y=-19/12

3x+3y=-11
3x+3(-19/12)=-11
3x-19/4=-11 |+19/4
3x=-11+19/4
3x=-25/4 |/3
x=-25/12

ODP: x=-²⁵/₁₂ y=-¹⁹/₁₂

. b)
x-1/4+2=y |-2, +1/4
y-3/3+5=x |-5, +1

x-y=-7/4
y-x=-4

0=-23/4

ODP: To nie jest równanie.

. c)
x+5/2+2y-1/3=4 |*6
3x+1/2+5y+2/4=5 |*2

6x+15+12y-2=24
6x+1+10y+1=10

12y+6x+13=24 |-13
10y+6x+2=10 |-2

12y+6x=11
10y+6x=8 |/-1

12y+6x=11
-10y-6x=-8

2y=3
y=3/2

10y+6x=8
10(3/2)+6x=8
15+6x=8 |-15
6x=-7 |/6
x=-7/6


ODP: x=-⁷/₆ y=³/₂

. d)
x+6/3+3y+1/2=5 |*6
y+1/2+x+5/8=2 |*8

6x+12+18y+3=30
8y+4+8x+5=16

18y+6x+15=30 |-15
8y+8x+9=16 |-9

18y+6x=15
8y+8x=7 |-8y

8x=7-8y |/8
x=7/8-y

18y+6(7/8-y)=15
18y-6y+21/4=15 |-21/4
12y=15-21/4
12y=39/4 |/12
y=13/6

ODP: x=¹/₁₆ y=¹³/₁₆

. e)
x+2/2-y-2/4=3 |*2
x-2/2-3y+1/7=0 |*7

2x+2-2y-1=3 |+1,-2
7x-7-21y+1=0 |+7,-1

2x-2y=5
7x-21y=6 |/7

2x-2y=5
x-3y=6/7

2x-2y=5
x=6/7+3y

2(6/7+3y)-2y=5
x=6/7+3y

12/7+4y=5 |-(12/7), /4
x=6/7+3y

y=(5-12/7)/4
x=6/7+3y

y=23/28
x=6/7+3y

y=23/28
x=6/7+3(23/28)

y=23/28
x=6/7+69/28

y=23/28
x=93/28

ODP: x=⁹³/₂₈ y=²³/₂₈

Answer 2

A)x+5/3-(1-y)=-3
y+5/2-(x-1)=4

x+5/3-1+y=-3
y+5/2-x+1=4 +
--------------------------
2y+5/3+5/2+1=1 /-31/6
2y=(-25/6) /:2
y=(-25/12)=(-2i1/12)

x+5/3-(1-(-25/12))=-3
x+5/3-27/12=-3 /+7/12
x=(-2i5/12)

Answer 3

A)
x+5/3-(1-y)=-3
y+5/2-(x-1)=4

x+y= -3-5/3+1
-x+y= 4-5/2-1

x+y= -3 i 2/3
-x+y= 1/2

x= -11/3-y
-(-11/3-y) +y =1/2

x= -11/3-y
11/3+y+y= 1/2

x= -11/3-y
2y= 1/2 - 11/3

x= -11/3-y
2y= 3/6 -22/6

x= -11/3-y
2y= -19/6

x= -11/3-y
y= -11/6 * 1/2

x= -11/3-y
y= -11/12

x= -11/3 - (-11/12)= -44/12 + 11/12 = - 33/12


x= -33/12
y= -11/12 ( można wydzielać całości, ale do sprawdzenia chyba lepiej zostawić w ułamkach)

b)
x-1/4+2=y
y-3/3+5=x


x-y= -2+1/4
-x +y = -5 +3/3

x-y= -7/4
-x+y = - 4 (3/3 to jedna całość)

x= - 7/4 +y
-(- 7/4 +y) +y = -4


x= - 7/4 +y
7/4 - y +y= -4


x= - 7/4 +y
0 = - 4 -7/4

( nie ma tu pomyłki w tekście zadania? albo układ równań nie ma rozwiązań)



c)
x+5/2+2y-1/3=4
3x+1/2+5y+2/4=5

x+2y = 4 -5/2 +1/3
3x+5y = 5 -1/2-2/4

x+2y= 4- 15/6 + 2/6
3x+5y= 5-2/4 -2/4

x+2y = 4-13/6
3x+5y= 5-1

x+2y= 11/6
3x+5y= 4

x= 11/6-2y
3*(11/6-2y) +5y =4

x= 11/6-2y
33/6 - 6y + 5y = 4

x= 11/6-2y
-y= 4- 33/6

x= 11/6-2y
-y= -9/6

x= 11/6-2y
y= 3/2

x= 11/6 - 2* 3/2= 11/6 -3= - 7/6

x= -7/6
y=3/2


d)
x+6/3+3y+1/2=5
y+1/2+x+5/8=2

x+3y =5 -2 -1/2
x+y= 2 -1/2-5/8

x+3y= 2 i 1/2
x+y= 2-9/8

x+3y= 5/2
x+y= 9/8

x= 5/2 - 3y
5/2 - 3y +y=9/8

x= 5/2 - 3y
-2y= 9/8 - 20/8

x= 5/2 - 3y
-2y= -11/8 / (-1)

x= 5/2 - 3y
y= 11/8 * 1/2

x= 5/2 - 3y
y= 11/16
x= 5/2 - 3* 11/16= 5/2 - 33/16 = 40/16-33/16= 7/16

x=7/16
y=11/16


e)
x+2/2-y-2/4=3
x-2/2-3y+1/7=0

x-y= 3 - 1 +2/4
x-3y= 1 - 1/7

x-y= 2 i 2/4
x-3y= 6/7

x-y =10/4
x-3y= 6/7

x= 10/4 +y
x-3y= 6/7

x= 10/4 +y
10/4 +y -3y=6/7

x= 10/4 +y
- 2y = 6/7 - 10/4

x= 10/4 +y
-2y= 24/28 - 70/28

x= 10/4 +y
-2y= - 46/28 /*(-1)

x= 10/4 +y
y= 46/56

x= 10/4 +y
y= 23/28

x= 10/4 +23/28= 70/28 + 23/28= 93/28

x=93/28
y=23/28