Решить системы 1. {16y^2 - 25x^2=8 4y + 5x= -2 2. {x\3y + 3y\x = 10\3 x^2 - 9y^2 = 8

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16y^2 - 25x^2 = 8
4y + 5x = -2

From the second equation, we can express x in terms of y:
x = (-2 - 4y) / 5

Substitute x into the first equation:
16y^2 - 25((-2 - 4y) / 5)^2 = 8
16y^2 - (4/5)^2 (25y^2 + 20y + 4) = 8
16y^2 - (4/5)^2 25y^2 - 20(4/5)y - 4 = 8
16y^2 - (16/25)25y^2 - 16y - 4 = 8
16y^2 - 16y^2 - 16y - 4 = 8
-16y - 4 = 8
-16y = 12
y = -3/4

Now substitute y back into x = (-2 - 4y) / 5
x = (-2 - 4(-3/4)) / 5
x = (-2 + 3) / 5
x = 1/5

Therefore, the solutions are x = 1/5 and y = -3/4.

2.
x/3y + 3y/x = 10/3
x^2 - 9y^2 = 8

Rewrite the first equation with a common denominator:
(x^2 + 9y^2) / (3xy) = 10/3

Now substitute x^2 - 9y^2 = 8 into the equation:
(8 + 9y^2) / (3y * y) = 10/3
(8 + 9y^2) / 3y^2 = 10/3
8 + 9y^2 = 10y^2
y^2 = 8

y^2 = 8
y = ±√8
y = ±2√2

Substitute y back into x^2 - 9y^2 = 8:
x^2 - 9(2√2)^2 = 8
x^2 - 36*2 = 8
x^2 - 72 = 8
x^2 = 80
x = ±√80
x = ±4√5

Therefore, the solutions are x = ±4√5 and y = ±2√2.