Question

Rozwiąż układ równań dwoma metodami
a.18x-21y=2
24x-15y=7

Answer 1

A.
Metoda przeciwnych współczynników
18x-21y=2 / * - 12
24x-15y=7 / * 9

- 216x + 252 y = -24
216 x -135 y = 63
....................dodajemy stronami
117y = 39 /117
y = 39/117 = 1/3
Podstawiamy y do równania
18x-21y=2
18x - 21 * 1/3 = 2
18x - 7 = 2
18x = 2 + 7
18x = 9 /:18
x = 9/18 = 1/2

Metoda podstawiania
18x-21y=2
24x-15y=7

18x = 2 + 21y / :18
24x-15y=7

x = 1/9 + 21/18y
24 * (1/9 + 21/18y) - 15y = 7

x = 1/9 + 21/18y
24/9 + 28y - 15y = 7

x = 1/9 + 21/18y
13y = 7 - 2 i 2/3

x = 1/9 + 21/18y
13y = 4 i 1/3

x = 1/9 + 21/18y
13y = 13/3 /:13

x = 1/9 + 21/18y
y = 13/3 * 1/13

x = 1/9 + 21/18y
y = 1/3

x = 1/9 + 21/18 * 1/3
y = 1/3

x = 2/18 + 7/18
y = 1/3

x = 9/18 = 1/2
y = 1/3