г) {lg (x²+y²) = 1+lg 13, lg (x+y) = lg (x-y)+lg 8.

г) Решим систему уравнений:

{lg (x^2+y^2) = 1+lg 13,

{lg (x+y) = lg (x-y)+lg 8.

{lg (x^2+y^2) = lg 10+lg 13,

{lg (x+y) = lg (x-y)+lg 8.

{lg (x^2+y^2) = lg 130,

{lg (x+y) = lg 8(x-y).

x^2+y^2 = 130,

x+y = 8(x-y)

x^2+y^2 = 130,

x+y = 8x-8y

x^2+y^2 = 130,

7x = 9y

x^2+y^2 = 130,

x = \frac{9y}{7}

(\frac{9y}{7})^2+y^2 = 130,

\frac{81y^2}{49}+y^2 = 130,

\frac{81y^2+49y^2}{49} = 130,

\frac{130y^2}{49} = 130,

y^2 = 49,

y = ±7

y = 7

y = -7

x = \frac{9\cdot7}{7} = 9,

x = \frac{9\cdot(-7)}{7} = -9,

lg (x+y) = lg (x-y)+lg 8.

lg (9+7) = lg (9-7)+lg 8.

lg 16 = lg 2+lg 8.

lg 16 = lg 16.

1,204 = 1,204.

lg (-9+(-7)) = lg (-9-(-7))+lg 8.

lg (-16) = lg (-2)+lg 8- не имеет смысла.

Ответ: x=9, y=7