Решите систему уравнений

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

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

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

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)