Question

Решите систему уравнений
a)[ x-y=5
[ x²+y²=25

b) [ 5xy-6=14
[ 6x-3y=6

Answer 1

Ответ:

a) y = 5 и y = -5. b) x = -3, y = 4.

Объяснение:

a)
x - y = 5

x + y = -5.

x² + y² = 25

x + y = -5

x = (-5 - y)

x² + y² = 25:

(-5 - y)² + y² = 25

25 - 10y + y² = 25

y² - 10y = 0

(y - 5)(y + 5) = 0

y = 5 и y = -5.

b)
5xy - 6 = 14

5xy + 6 = -14.

6x - 3y = 6

5xy + 6 = -14

x = (-6 - 3y) / 6

5xy + 6 = -14:

(-6 - 3y) / 6 * 5y + 6 = -14

(-30 - 15y + 6) / 6 = -14

-30 - 15y + 6 = -84

-15y = -60

y = 4

x = (-6 - 3 * 4) / 6

x = (-6 - 12) / 6

x = -18 / 6

x = -3

x = -3, y = 4.