Question

Rozwiąż układ równań​

Answer 1

Odpowiedź:

c)

(3x - 1)/2 - (4y - 7)/3 = 2 | * 6

(3y - 6)/4 - (5 - x)/6 = - 1 5/12 = - 17/12 | * 12

3(3x - 1) - 2(4y - 7) = 12

3(3y - 6) - 2(5 - x) = - 17

9x - 3 - 8y + 14 = 12

9y - 18 - 10 + 2x = - 17

9x - 8y + 11 = 12

2x + 9y - 28 = - 17

9x - 8y = 12 - 11

2x + 9y = - 17 + 28

9x - 8y = 1 | * 9

2x + 9y = 11 |* 8

81x - 72y = 9

16x + 72y = 88

dodajemy równania

81x + 16x - 72y + 72y = 9 + 88

97x = 97

x = 97 : 97 = 1

9x - 8y = 1

9 * 1 - 8y = 1

9 - 8y = 1

- 8y = 1 - 9

- 8y = - 8

8y = 8

y = 8 : 8 = 1

Odp: x = 1 , y = 1

d)

(2x - y)/5 - ( y + 2x)/4 = 1,2 | * 20

(2x + 3y)/12 - (4x - y)/8 = 0,25 | * 24

4(2x - y) - 5(y + 2x) = 24

2(2x + 3y) - 3(4x - y) = 6

8x - 4y - 5y - 10x = 24

4x + 6y - 12x + 3y = 6

- 2x - 9y = 24

- 8x + 9y = 6

dodajemy równania

- 2x - 8x - 9y + 9y = 24 × 6

- 10x = 30

10x = - 30

x = - 30 : 10 = - 3

- 2x - 9y = 24

- 2 * (- 3) - 9y = 24

6 - 9y = 24

- 9y = 24 - 6 = 18

9y = - 18

y = - 18 : 9 = - 2

Odp: x = - 3 , y = - 2