Question

Rozwiąż ukł. równań metodą podstawiania.

2x+y=8

4x-y=10

y=-2x+8

4x-(-2x+8)=10

3x+2y=-3

7x+2y=1

2x-3y=7

4x+1/2y=1

4x-6y=0

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

Answer 1

2x + y = 8

4x - y = 10                   | + y

2x + y = 8

4x - 10 = y

2x + 4x - 10 = 8

4x - 10 = y

6x = 18

4x - 10 = y

x = 3

12 - 10 = y

x = 3

y = 2

 

3x+2y=-3                  | - 2y         | : 3

7x+2y=1 

x = - 1 - 2/3y

7x + 2y = 1

x = -1 - 2/3y

7*(-1 - 2/3y) + 2y = 1

x = -1 - 2/3y

-7 - 14/3y + 6/3y = 1

x = - 1 - 2/3y

- 8/3y = 8                       | *3

x = - 1 - 2/3y

y = -3

x = - 1 - 2/3 * (-3) = -1 +2 = 1

y = -3

x = 1

 

2x-3y=7

4x+1/2y=1               | * 2

2x - 3y = 7

y = 2 - 8x

2x - 3*(2-8x) = 7

y = 2 - 8x

2x - 6 + 24x = 7

26x = 13

x = 0,5

y = 2 - 8 * 0,5 = 2 - 4 = -2

x = 0,5

y = -2

 

4x-6y=0

2/3x+1/2y=1/3                   | *6

4x - 6y = 0

4x - 2 = - 3y

4x - 6y = 0

-4/3x + 2/3 = y

4x - 6 * (-4/3x + 2/3) = 0

-4/3x + 2/3 = y

4x + 8x = 4

12x = 4

x = 4/12 = 1/3

-4x + 2 =  3y

-4 * 1/3 + 2 = 3y

-4/3 + 2 = 3y

y = 2/9

x = 1/3

 

Answer 2

y=-2x+8

4x-(2x+8)=10

4x-2x-8=10

2x=10+8

2x=18   /:2

x=9

y=-2*9+8

y=-18+8

y=26

 

3x+2y=-3

7x+2y=1

2y=-3-3x   /:2

y=-3/2-3/2x

 

7x+2*(-3/2-3/2x)=1

7x-3-3x=1

7x-3x=1+3

4x=4   /:4

x=1

y=-3/2-3/2*1

y=-6/2

y=-3

 

2x-3y=7

4x+1/2y=1

-3y=7-2x   /:(-3)

y=-7/3+2/3x

4x+1/2(-7/3+2/3x)=1

4x-7/6+1/3x=1

4i1/3x=1+7/6

13/3x=13/6   /*3/13

x=13/6*3/13

x=39/78

x=1/2

 

4x-6y=0

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

-6y=-4x   /:(-6)

y=2/3x

2/3x+1/2*2/3x=1/3

2/3x+1/3x=1/3

x=1/3

y=2/3*1/3=2/6=1/3