24(x-y)=x*y 5(x-y)=x+y

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вопрос

To solve these equations for x and y, we can use the substitution or elimination method.

First, let's solve the first equation:

24(x-y) = x*y
24x - 24y = xy
24x = xy + 24y
24x = y(x + 24)
y = 24x / (x + 24)

Now, let's substitute y = 24x / (x + 24) into the second equation:

5(x - 24x / (x + 24)) = x + 24
5((x^2 - 24x) / (x + 24)) = x + 24
5x^2 - 120x = x^2 + 24x + 24(5)
5x^2 - x^2 - 120x - 24(5) - 24x = 0
4x^2 - 144x - 120 = 0
x^2 - 36x - 30 = 0

Now, we can solve for x using the quadratic formula:

x = [36 ± sqrt(36^2 - 4(1)(-30)]) / 2(1)
x = [36 ± sqrt(1296 + 120]) / 2
x = [36 ± sqrt(1416)] / 2
x = [36 ± 37.66] / 2

Therefore, the solutions for x are x = 1.83 or x = 34.17.

Now, we can substitute these values of x back into y = 24x / (x + 24) to find the corresponding values of y:

For x = 1.83:
y = 24(1.83) / (1.83 +24)
y = 43.92 / 25.83
y = 1.70

Therefore, for x = 1.83, y = 1.70.

For x = 34.17:
y = 24(34.17) / (34.17 + 24)
y = 820.08 / 58.17
y = 14.11

Therefore, for x = 34.17, y = 14.11.

In conclusion, the solutions for this system of equations are x = 1.83, y = 1.70 and x = 34.17, y = 14.11.