Question

zadanie 6 strona 102, matematyka z plusem (niebieski podręcznik) klasa 2 gimnazjum.

treść :

Rozwiąż podane układy metodą podstawiania.

a) 2x+3y=0,5 b) 2x+y=14 c) 3x+4y=2

3x+y= -1 8x+ jedna druga y = 35 5x+7y=1

Answer 1

a) 2x+3y=0,5

3x+y= -1

y=-1-3x

2x+3(-1-3x)=0,5

2x-3-9x=0,5

-7x=3,5/:(-7)

x=-1/2

y-1-3(-1/2)

y=1/2

b) 2x+y=14

8x+ 1/2 y = 35

y=14-2x

8x+1/2(14-2x)=35

8x+7-x=35

7x=28/:7

x=4

y=14-2*4

y=6

c) 3x+4y=2

5x+7y=1

4y=2-3x/:4

y=0,5-0,75x

5x+7(0,5-0,75x)=1

5x+3,5-5,25x=1

-0,25x=-2,5/*(-4)

x=10

y=0,5-0,75*10

y=-7

Answer 2

2x+3y=0,5                       x=-0,5

3x+y=-1                           y=0,5

2x+3y=0,5

y=-1-3x                                2·(-0,5)+3·0,5=0,5

2x+3(-1-3x)=0,5                   3·(-0,5)+0,5=-1

y=-1-3x                                -1+1,5=0,5

2x-3-9x=0,5                          -1,5+0,5=-1

y=-1-3x                                  0,5=0,5

-7x=0,5+3                                -1=-1

y=-1-3x

-7x=3,5/:-7

y=-1-3x

x=-0,5

y=-1-3(-0,5)

x=-0,5

y=-1+1,5

x=-0,5

y=0,5

 

2x+y=14

8x+½y=35                     x=4

y=14-2x                        y=6

8x+½(14-2x)=35           2·4+6=14

y=14-2x                        8·4+½·6=35

8x+7-x=35                      8+6=14

y=14-2x                        32+3=35

7x=35-7                        14=14

y=14-2x                          35=35

7x=28/:7

y=14-2x

x=4

y=14-2·4

x=4

y=14-8

x=4

y=6

 

 

3x+4y=2                       y=-7

5x+7y=1                       x=10

3x=2-4y/:3                   3·10+4·(-7)=2

5x+7y=1                        5·10+7·(-7)=1

x=(2-4y):3                      30-28=2

5·(2-4y):3+7y=1              50-49=1

x=(2-4y):3                          2=2

(10-20y):3+7y=1                 1=1

x=(2-4y):3

(10-20y):3=1-7y//·3

x=(2-4y):3

10-20y=3-21y

x=(2-4y):3

-20y+21y=3-10

x=(2-4y):3

y=-7

x=(2-4·(-7)):3

y=-7

x=(2+28):3

y=-7

x=30:3

y=-7

x=10