Question

Witam,

wyznacz wartości parametrów a, b, c. W tym celu rozwiąż układ równań:

a + b + c = 5

4a - 2b + c = 2

9a + 3b + c = 27

Answer 1

a + b + c = 5     /*(-1)

4a - 2b + c = 2

 

-a - b - c = -5

4a - 2b + c = 2

--------------------------

3a - 3b = -3

a - b = -1

a = b - 1

 

a + b + c = 5

b - 1 + b + c = 5

2b = c + 6

2b - 6 = c

 

 

9a + 3b + c = 27

9 (b - 1) + 3b + 2b - 6 = 27

9b - 9 + 3b + 2b - 6 = 27

14b = 27 + 15

14b = 42

b = 3

 

a = b - 1

a = 3 - 1

a = 2

 

2b - 6 = c

c = 2 * 3 - 6

c = 6 - 6

c = 0

Answer 2

a + b + c = 5          -----------c=5-a-b

4a - 2b + c = 2

9a + 3b + c = 27

 

4a-2b+5-a-b=2

9a+3b+5-a-b=27

 

3a-3b=2-5          ------ 3a=-3+3b   --------a=b-1

8a+2b=27-5

 

8(b-1)+2b=22

8b-8+2b=22

10b=22+8

10b=30

b=30/10

b=3

a=b-1=3-1

a=2

c=5-a-b=5-2-3=5-5

c=0

a=2      b=3     c=0

spr.

2+3=5

4*2-2*3+0=8-6=2

9*2+3*3+0=18+9=27