Question

b.

{3/4(x-3)-(3-y)=-1

1/2 (x-5)+2 (y+1)=-2

c.

{1/4(2x-4)-(y-3)=-1

2(y-1)-1/3(x-1)=7

d.

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

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

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Answer 1

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

 

3/4x-9/4-3+y=-1

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

 

0,75x-2,25-3+y=-1

0,5x-2,5+2y+2=-2

 

0,75x+y=-1+2,25+3

0,5x+2y=-2+2,5-2

 

0,75x+y= 4,25 /*(-2)

0,5x+2y=-1,5

 

-1,5x-2y=-8,5

0,5x+2y=-1,5

----------------- +

-x=-10 /*(-1)

x=10

 

0,75x+y=4,25

0,75*10+y=4,25

7,5+y=4,25

y=4,25-7,5

y=-3,25

 

x=10

y=-3,25

 

c)

{1/4(2x-4)-(y-3)=-1
2(y-1)-1/3(x-1)=7

 

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

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

 

1/2x-y=-1-2

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

 

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

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

 

x-2y=-6

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

--------------------- +

2/3x=2 2/3

2/3x=8/3*3/2

x=4

 

1/2x-y=-3

1/2*4-y=-3

2-y=-3

-y=-3-2

-y=-5 /*(-1)

y=5

 

x=4

y=5

 

d)

{1/3(x+1)-3(2y-1)=11
2(3-x)+1/4(y+1)=-4

 

1/3x+1/3-6y+3=11

6-2x+1/4y+1/4=-4

 

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

-2x+1/4y=-4-6-1/4

 

1/3x-6y=7 2/3

-2x+1/4y=-10 1/4 /*24

 

1/3x-6y=7 2/3

-48x+6y=-246

---------------- +

-47 2/3x= -238 1/3

-143/3x=-715/3 /*(-3/143)

x=5

 

-2x+1/4y=-10 1/4

-2*5+1/4y=-10 1/4

1/4y=-10 1/4+10

1/4y=-1/4 /*4/1

y=-1

 

x=5

y=-1

 

 

 

 

Answer 2

{3/4(x-3)-(3-y)=-1

1/2 (x-5)+2 (y+1)=-2

 

3/4x-9/4-3+y=-1

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

3/4x+y=-1+9/4+3

1/2x+2y=5/2

3/4x+y=4i 1/4

1/2x+2y=5/2

3/4x+y=17/4|razy (-2)

1/2x+2y=5/2

 

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

+

1/2x+2y=5/2
____________

-3/2-2y+1/2x+2y=8 i 1/2+5/2 teraz skracamy

-x=-6|razy (-1)

x=6

1/2x+2y=5/2

x=6

3+2y=5/2

x=6

2y=5/2-3

x=6

y=1/4