Question

Zadanie 9. Rozwiąż układy równań metodą podstawiania.

a) 2x - 2y = 7
4x + 3y = 21

b) 0,4x + 0,3y = 1,4
0,1x + 3y = 2,3

c) 2x + 3y = 14
3x - 2y = 8

d) jedna druga x - 2y = 8
2x + 5y = 6

e) jedna druga x - trzy czwarte y = 0
dwie trzecie x + jeden i jedna czwarta y = 9

f) 3x + 4y = jeden i dwie trzecie
6x + 3y = jeden i jedna czwarta


Z góry bardzo dziękuję za rozwiązanie zadania.

Answer 1

Zad.1
a) 2x - 2y = 7
4x + 3y = 21

2x=7+2y /2
4x+3y=21

x=3,5 +y
4(3,5+y)+3y=21

x=3,5+y
14+4y+3y=21

x=3,5+y
7y=7

x=3,5+y
y=1

x=3,5+1
y=1

x=4,5
y=1

bx = 3, y = 2/3 .

c)2x + 3y =14
3x - 2y = 8

2x=14-3y /2
3x-2y=8

x=7-1,5y
3(7-1,5y)-2y=8

x=7-1,5y
21-4,5y-2y=8

x=7-1,5y
-6,5y=-13 /(-6,5)

x=7-1,5y
y=2

x=7- 1,5(2)
y=2

x=4
y=2

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

0,5x=8+2y /0,5
2x+5y=6

x=16+4y
2(16+4y)+5y=6

x=16+4y
32+8y+5y=6

x=16+4y
13y=-26 /13

x=16+4y
y=-2

x=16+4(-2)
y=-2

x=8
y=-2

Answer 2

A)
2x-2y=7
4x+3y=21

2x=7+2y (:2)
3y=21-4x (:3)

x=3,5+y
y=7-4/3x

x=3,5+7-4/3x
y=7-4/3x

x+4/3x=10,5
y=7-4/3x

2 1/3x=10,5 (:7/3)
y=7-4/3x

x=21/2*3/7
y=7-4/3x

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

x=3
y=7-4=3

x=3
y=3

b)
0,4x+0,3y=1,4
0,1x+3y=2,3

0,3y=1,4-0,4x
0,1x=2,3-3y

y=14/3-4/3x
x=23-30y

y=14/3-4/3(23-30y)
x-23-30y

y=14/3-92/3+40y
x=23-30y

y-40y=-78/3
x=23-30y

-39y=-26
x=23-30y

y=2/3
x=23-30(2/3)

y=2/3
x=25-20

y=2/3
x=5


c)
2x+3y=14
3x-2y=8

3y=14-2x
3x=8+2y

y=14/3-2/3x
x=8/3+2/3y

y=14/3-2/3(8/3+2/3y)
x=8/3+2/3y

y=14/3-16/6-4/6y
x=8/3+2/3y

y+4/6y=28/6-16/6
x=8/3+2/3y

1 2/3y=8/6
x=8/3+2/3y

y=4/3:5/3
x=8/3+2/3y

y=4/5
x=8/3+2/3(4/5)

y=4/5
x=8/3+8/15

y=4/5
x=48/15

y=4/5
x=3 1/5

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

1/2x=2y+8
5y=6-2x

x=4y+16
y=6/5-2/5x

x=4y+16
y=6/5-2/5(4y+16)

x=4y+16
y=6/5-8/5y+32/5

x=4y+16
y+8/5y=6/5+32/5

x=4y+16
13/5y=38/5

x=4y+16
y=38/5*5/13

x=4y+16
y=38/13

x=4(38/13)+16
y=2 12/13

x=11 9/13+16
y=2 12/13

x=27 9/13
y=2 12/13

e)
1/2x-3/4y=0
2/3x+1 1/4y=9

1/2x=3/4y
5/4y=9-2/3x

x=3/2y
y=9(4/5)-2/3x(4/5)

x=3/2y
y=36/5-8/15x

x=3/2y
y=36/5-8/15(3/2y)

x=3/2y
y=36/5-4/5y

x=3/2y
y+4/5y=36/5

x=3/2y
9/5y=36/5

x=3/2y
y=36/5*5/9

x=3/2y
y=4

x=3/2*4
y=4

x=6
y=4
f)
1/2x+4y=1 2/3
6x+3y=1 1/4

x=10/3-8y
3y=5/4-6x

x=10/3-8y
y=15/4-2x

x=10/3-8(15/4-2x)
y=15/4-2x

x=10/3-30+16x
y=15/4-2x

x-16x=26 2/3
y=15/4-2x

-15x=26 2/3
y=15/4-2x

x=80/3:(-15)
y=15/4-2x

x=-16/15
y=15/4-2(-16/15)

x=-16/15
y=15/4+32/15

x=-1,06(6)
y=353/60=5,88

x=-1,06(6)
y=5,88