Question

Решите систему уравнений

Answer 1

$left { {{5^{x}+5^{y}  = 30} atop {x+y=3}} right.$

$left { {{5^{x} + 5^{y} = 30} atop {x=3-y}} right.$

$5^{3-y} + 5^{y} = 30$

y = 2

y = 1

x = 3 - 2

x = -3 -1

x = 1

x = 2

(x₁, у₁) = (1 , 2)

(х₂ , у₂) = (2 , 1)

$left { {{5^{1}+5^{2} = 30 } atop {1+2=3}} right.$

$left { {{5^{2}+5^{1} = 30 } atop {2+1 = 3}} right.$

$left { {{30 = 30} atop {3=3}} right.$

$left { {{30=30} atop {3=3}} right.$

(х₁ , у₁) = (1 , 2)

(х₂, у₂) = (2 , 1)

Answer 2

Можете, пожалуйста, объясните, как вы нашли y=1, y=2

Answer 3

x=log(5,30-5^y)

Answer 4

x = log(5,5*(6-1^y))=log(5,5) + log(5,5) = 2

Answer 5

2 + y = 3 => y = 1

Answer 6

Либо наоборот y = 2 ; x = 1