Question

Rozwiąż układ równań . (METODĄ PRZECIWNYCH WSPÓŁCZYNNIKÓW !! )

a) 2(x+y)-(x-y)=4
3(x-2y)+4(x+y)=5


b) 4(x+2y)-3(x-y)=42
2(y-x)+3(x-y)=-6

c) 3(x+y)-2(x-2y)=5
2(x+2)-4(y+1)=-8

d) 2(3x+4y)-7(y-x)=-37
4(x+2)-(y-4)=-2

(METODĄ PRZECIWNYCH WSPÓŁCZYNNIKÓW !! )

Answer 1

A) 2(x+y)-(x-y)= 4
2x+2y-x+y= 4
2x-x+2y+y=4
x+3y=4

3(x-2y)+4(x+y)=5
3x+4x-6y+4y=5
3x-6y+4x+4y=5
7x-2y=5

b) 4(x+2y)-3(x-y)=42
4x+8y-3x+3y=42
4x-3x+8y+3y=42
x+11y=42

2(y-x)+3(x-y)=6
2y-2x+3x-3y=6
2y-3y-2x+3x=6
-y+x=6

c) 3(x+y)-2(x-2y)=5
3x+3y-2x+4y=5
3x-2x+3y+4y=5
x+7y=5

2(x+2)-4(y+1)=-8
2x+4-4y-4=-8
2x-4y=-8

d) 2(3x+4y)-7(y-x)=-37
6x+8y-7y+7x=-37
6x+7x+8y-7y=-37
13x+y=-37

4(x+2)-(y-4)=-2
4x+8-y+4=-2
4x+12-y=-2

Answer 2

A)

2(x+y) - (x-y) = 4
3(x-2y) + 4(x+y) = 5

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

x + 3y = 4 / * 2
7x - 2y = 5 / * 3

2x + 6y = 8
21x - 6y = 15

23x = 23 / : 23
x = 1

1 + 3y = 4
x = 1

3y = 4 - 1
x = 1

3y = 3 / :3
x = 1

x = 1
y = 1

b)

4(x+2y) - 3(x-y) = 42
2(y-x) + 3(x-y) = - 6

4x + 8y - 3x + 3y = 42
2y - 2x + 3x - 3y = - 6

x + 11y = 42
x - y = - 6 / * (-1)

x + 11y = 42
- x + y = 6

12y = 48 / :12
y = 4

x - y = - 6
y = 4

x - 4 = -6
y = 4

x = - 6 + 4
y = 4

x = - 2
y = 4

c)

3(x+y) - 2(x-2y) = 5
2(x+2) - 4(y+1) = - 8

3x + 3y - 2x + 4y = 5
2x + 4 - 4y - 4 = - 8

x + 7y = 5
2x - 4y = - 8 / :2

x + 7y = 5
x - 2y = - 4 / * (-1)

x + 7y = 5
- x + 2y = 4

9y = 9 / : 9
y = 1

x + 7 = 5
y = 1

x = - 2
y = 1

d)

2(3x+4y) - 7(y-x) = -37
4(x+2) - (y-4) = -2

6x + 8y - 7y + 7x = - 37
4x + 8 - y + 4 = - 2

13x + y = - 37
4x - y = - 2 - 4 - 8

13x + y = - 37
4x - y = - 14

17x = - 51 / : 17
x = 3

12 - y = - 14
x = 3

12 + 14 = y
x = 3

x = 3
y = 26

PS. Mam nadzieję że pomogłam ;)