Question

Rozwiązywanie układów równan metodą podstawiania ;

½x-2y=8

2x+5y=6

3x+4y=1⅔

6x+3y=1¼

x=-y

x-y=6

-3x=2y

y=1-x

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

10x-2y=18

x+y=0

x-y=10

Answer 1

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

2x+5y=6

 

1/2x=8+2y

2x+5y=6

 

x=4+y

2(4+y)+5y=6

 

x=4+y

8+2y+5y=6

 

x=4+y

8+7y=6

 

x=4+y

7y=-2 /:7

 

x=4+y

y=-2/7

 

x=4=(-2/7)

y=-2/7

 

x=3 5/7

y=-2/7

 

 

c)

x=-y

x-y=6

 

x=-y

-y=6-x/(-1)

 

x=-y

y=-6+x

 

x=-(-6+x)

y=-6+x

 

-6+x

y=-6+x

 

x=6-x

y=-6+6-x

 

x=6-x /+x

y=-x

 

2x=6/:2

y=-x

 

x=3

y=-3

 

d)

-3x=2y

y=1-x

 

-3x=2(1-x)

y=1-x

 

-3x=2-2x/+2x

y=1-x

 

-x=2/(-1)

y=1-x

 

x=-2

y=1-(-2)

 

x=-2

y=1+2

 

x=-2

y=3

 

e)

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

10x-2y=18

 

4x-8-y+2=1

10x-2y=18

 

4x-6-y=1/+6

10x-2y=18

 

4x-y=7/-4x

10x-2y=18

 

-y=7-4x/(-1)

10x-2y=18

 

y=-7+4x

10x-2(-7+4x)=18

 

y=-7+4x

10x+14-8x=18

 

y=-7+4x

2x+14=18 /-14

 

y=-7+4x

2x=4 /:2

 

y=-7+4x

x=2

 

y=-7+4*2

x=2

 

y=-7+8

x=2

 

y=1

x=2

 

f)

x+y=0

x-y=10 /+y

 

x=y=0

x=10+y

 

10+y+y=0

x=10+y

 

10+2y=0 /-10

x=10+y

 

2y=-10 /:2

x=10+y

 

y=-5

x=10+(-5)

 

y=-5

x=10-5

 

y=-5

x=5