Question

СРОЧНО:Розв'яжіть систему рівнянь{xy=12,2x-y=2.​ Смотреть ответ dasha121264 dasha121264 Ответ: xy=12 x=2/y 2x-y=2 2x-y-2=0

Answer 1

System of Equations Solution

To solve the system of equations:

1. xy = 12 2. 2x - y = 2

We can use the method of substitution or elimination. Let's use the substitution method.

From equation 1, we can express x in terms of y:

xy = 12 x = 12/y

Now, substitute the value of x in equation 2:

2(12/y) - y = 2 24/y - y = 2 (24 - y^2)/y = 2

To simplify further, multiply both sides of the equation by y:

24 - y^2 = 2y y^2 + 2y - 24 = 0

Now, we have a quadratic equation. We can solve it by factoring or using the quadratic formula. Factoring the equation, we get:

(y + 6)(y - 4) = 0

Setting each factor equal to zero, we have two possible values for y:

1. y + 6 = 0 y = -6

2. y - 4 = 0 y = 4

Now, substitute these values of y back into equation 1 to find the corresponding values of x:

For y = -6: x = 12/(-6) x = -2

For y = 4: x = 12/4 x = 3

Therefore, the solution to the system of equations is: x = -2, y = -6 x = 3, y = 4

Please let me know if you need any further assistance!