Question

Układy równań rozwiąż metodą podstawiania

a) x+2y=6

x-y=3

b) x+3y=12

2x-y=3

c)2x-y=5

3x=y-6

d)y-2x=6

y=3+x

Answer 1

a)x+2y=6
x-y=3
......
x=-2y+6
-2y+6-y=3
......
x=-2y+6
-3y=-3/:(-3)
.......
x=-2y+6
y=1
......
x=-2*1+6
y=1
......
x=4
y=1

Answer 2

A.

x+2y=6

x-y=3

 

x=3+y

3+y+2y=6

 

x=3+y

3y=6-3

 

x=3+y

3y=3/:3

 

x=3+y

y=1

 

x=3+1

y=1

 

x=4

y=1

 

-------------------

B.

x+3y=12

2x-y=3

 

x=12-3y

2(12-3y)-y=3

 

x=12-3y

24-6y-y=3

 

x=12-3y

-6y-y=3-24

 

x=12-3y

-7y=-21/:7

y=3

 

x=12-3*3

x=12-9

 

x=3

y=3

 

-------------------------------

C.

2x-y=5

3x=y-6

 

2x-5=y

3x=2x-5-6

 

2x-5=y

3x-2x=-5-6

 

2x-5=y

x=-11

 

2*(-11)-5=y

x=-11

 

-22-5=y

x=-11

 

x=-11

y=-27

 

---------------------------

D.

y-2x=6

y=3+x

 

3+x-2x=6

y=3+x

 

x-2x=6-3

y=3+x

 

-x=3/:(-1)

x=-3

 

y=3+(-3)

y=3-3

 

x=-3

y=0

 

:)