Question

Rozwiąż układy równań:
a) x+y=5
x-2y=-1



b) y-x=4
3(x+y)=24



c) x-2y=4
x+3=2y



d) 3x-1=y-2
4x-3=2(y-2)



e) 2(x+y)-(x-1)=y+2
x+y=1

Answer 1

A) x+y=5
x-2y=-1

x=5-y
5-y-2y=-1
-3y=-6
y=2
x=5-2=3

b) y-x=4
3(x+y)=24

y=4+x
3(x+4+x)=24
6x+12=24
6x=12
x=2
y=4+2=6

c) x-2y=4
x+3=2y
to mi jakoś nie wychodzi

d) 3x-1=y-2
4x-3=2(y-2)

4x-3=6x-2
-2x=1
x=-1/2
-2-3=2y-4
2y=-1
y=-1/2

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

Answer 2

A)
x+y=5
x-2y=-1

x=5-y
5-y-2y=-1

x=5-y
-3y=-1-5

x=5-y
-3y=-6 /:-3

x=5-y
y=2

x=5-2
y=2

x=3
y=2


b)
y-x=4
3(x+y)=24

y=4+x
3x+3y=24

y=4+x
3x+3(4+x)=24

y=4+x
3x+12+3x=24

y=4+x
6x=24-12

y=4+x
6x=12 /:6

y=4+x
x=2

y=4+2
x=2

y=6
x=2


d) 3x-1=y-2
4x-3=2(y-2)

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

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

y=1+3x
4x-3=2+6x+3x

y=1+3x
4x-6x-3x=2+3

y=1+3x
-5x=5 /:-5

y=1+3x
x=-1

y=1+3*(-1)
x=-1

y=1-3
x=-1

y=-2
x=-1

e)
2(x+y)-(x-1)=y+2
x+y=1

2x+2y-x+1=y+2
x=1-y

x+y=2-1
x=1-y

1-y+y=2-1
x=1-y

o=0
x=1-0

x=1