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*24x - 24y = x24x = xy + 2424x = y(x + 24y = 24x / (x + 24)
Now, let's substitute y = 24x / (x + 24) into the second equation:
5(x - 24x / (x + 24)) = x + 25((x^2 - 24x) / (x + 24)) = x + 25x^2 - 120x = x^2 + 24x + 24(55x^2 - x^2 - 120x - 24(5) - 24x = 4x^2 - 144x - 120 = x^2 - 36x - 30 = 0
Now, we can solve for x using the quadratic formula:
x = [36 ± sqrt(36^2 - 4(1)(-30)]) / 2(1x = [36 ± sqrt(1296 + 120]) / x = [36 ± sqrt(1416)] / 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 = 1.83y = 24(1.83) / (1.83 +24y = 43.92 / 25.8y = 1.70
Therefore, for x = 1.83, y = 1.70.
For x = 34.17y = 24(34.17) / (34.17 + 24y = 820.08 / 58.1y = 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.
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*
24x - 24y = x
24x = xy + 24
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 + 2
5((x^2 - 24x) / (x + 24)) = x + 2
5x^2 - 120x = x^2 + 24x + 24(5
5x^2 - x^2 - 120x - 24(5) - 24x =
4x^2 - 144x - 120 =
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]) /
x = [36 ± sqrt(1416)] /
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 / 25.8
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 / 58.1
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.