Question

Oblicz równania metodą podstawiania : a) x-y=2 x+2y=11 b) 2x-y=4 x-2y= -1 c) 2x-5y=2 y-2x=10

Answer 1

a)

x-y=2 

x+2y=11

 

x=2+y

2+y+2y=11

 

x=2+y

3y=9

 

x=2+y

y=3

 

x=5

y=3

 

b) 2x-y=4 

x-2y=-1

 

-y=4-2x

x-2y=-1

 

y=-4+2x

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

 

y=-4+2x

x+8-4x=-1

 

y=-4+2x

-3x=-9

 

y=-4+2x

x=3

 

y=-4+6

x=3

 

y=2

x=3

 

c) 2x-5y=2

y-2x=10

 

2x-5y=2

y=2x+10

 

2x-5(2x+10)=2

y=2x+10

 

2x-10x-50=2

y=2x+10

 

-8x=52

y=2x+10

 

x=-6,5

y=-13+10

 

x=-6,5

y=-3

 

 

Answer 2

a)

x-y=2

x+2y=11

 

x=2+y

2+y+2y=11

 

x=2+y

3y=11-2

 

x=2+y

3y=9/:3

 

x=2+y

y=3

 

x=2+3

y=3

 

x=5

y=3

 

b)

2x-y=4

x-2y= -1

 

2x-y=4

x=-1+2y

 

x=-1+2y

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

 

x=-1+2y

-2+4y-y=4

 

x=-1+2y

3y=4+2

 

x=-1+2y

3y=6/:3

 

x=-1+2y

y=2

 

x=-1+2*2

y=2

 

x=-1+4

y=2

 

x=3

y=2

c)

2x-5y=2

y-2x=10

 

2x-5y=2

y=10+2x

 

2x-5(10+2x)=2

y=10+2x

 

2x-50-10x=2

y=10+2x

 

-8x=52/:-8

y=10+2x

 

x=-52/8

y=10+2*(-52/8)

 

x=-52/8

y=10-52/4

 

x=-6,5

y=-3