Question

Rozwiąż układ równań metodą podstawiania. a) x-3y=1 2x-5y=7 b) 4x-3y=2 -2x+y=4 c) 2x+y=3 x-2y=4

Answer 1

A)x-3y=1 2x-5y=7 x=1+3y 2(3y+1)-5y=7 x=1+3y 6y+2-5y=7 x=1+3y y=5 x=1+3*5 y=5 x=16 y=5 b)4x-3y=2 -2x+y=4 4x-3y=2 y=4+2x 4x-3(4+2x)=2 y=4+2x 4x-12-6x=2 y=4+2x -2x=-10/:(-2) y=4+2x x=5 y=4+2*5= x=5 y=14 c)2x+y=3 x-2y=4 y=3-2x x-2(3-2x)=4 y=3-2x x-6+4x=4 y=3-2x 5x=10/:5 y=3-2x x=2 y=3-2*5 x=2 y=-7

Answer 2

a)

 

x-3y=1

2x-5y=7

 

x=1+ 3y
2x=7+5y / 2

x=1+ 3y

x=3,5+2,5Y

3,5+2,5y=1+3y

 

3,5 + 1 = 3y - 2,5y

 

4,5= 0,5y *2

y= 9

x= 1 + 3(9)
x= 28

 

x=28

y=9

b)

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

4x= 2 + 3y /2

y= 4 + 2x

 

2x= 1 + 1,5y

y= 4 + 2x

 

y= 4 +1 + 1,5y

2,5y = 5 /2,5

y=2

 

2=4+2x

 

2-4=2x

 

-2=2x /2

 

x=-1

y=2

 

c)

 

2x+y=3

x-2y=4

 

y=3-2x

x-2(3-2x)=4

 

x-6+4x=4

 

5x = 4 + 6

 

5x= 10 /2

 

x=2

 

2-2y=4

 

-2y=4-2

 

-2y=2 / -2

 

y=-2

x=2