Question

X*y=2400м² (x+y)*2=220м​

Answer 1

Метод подстановки

xy=2400

2x+2y=220

2x=220-2y

x=110-y

y(110-y)=2400

-y^2+110y=2400

y^2-110y+2400=0

d1=3025-2400=625, d1>0, значит 2 корня

y1=55+25=80, y2=55-25=30

Значит, x=110-80=30; x=110-30=80

Ответ: 30; 80.

Answer 2

To solve the system of equations:

1. X * Y = 2400 m²
2. (X + Y) * 2 = 220 m

Let's proceed step by step.

First, let's simplify the second equation by dividing both sides by 2: X + Y = 110 m

Now we have a system of equations:

1. X * Y = 2400 m²
2. X + Y = 110 m

To solve this system, we can use substitution or elimination method. Let's use the substitution method.

From equation 2, we can express X in terms of Y as X = 110 - Y.

Substituting this expression for X in equation 1, we get: (110 - Y) * Y = 2400

Expanding the equation: 110Y - Y² = 2400

Rearranging the equation and setting it equal to zero: Y² - 110Y + 2400 = 0

Now we can solve this quadratic equation for Y. Factoring it, we get: (Y - 40)(Y - 60) = 0

Setting each factor equal to zero: Y - 40 = 0 or Y - 60 = 0

Solving these equations, we find: Y = 40 or Y = 60

Now that we have the values of Y, we can substitute them back into equation 2 to find the corresponding values of X.

For Y = 40: X + 40 = 110 X = 110 - 40 X = 70

For Y = 60: X + 60 = 110 X = 110 - 60 X = 50

So the solutions to the system of equations are: X = 70, Y = 40 X = 50, Y = 60