Question

1/х+1/у=5/6{ х+у=5​

Answer 1

1/х + 1/у = 5/6 <=> х+у/х*у = 5/6

подставим х+у = 5 в уравнение повыше

5/х*у = 5/6 => х*у = 6

2;3 и 3;2 подходят и к уравнение х+у=5 и х*у = 6

Ответ: 2;3 и 3;2

Answer 2

To solve the system of equations:

1. 1/x + 1/y = 5/6
2. x + y = 5

We can use substitution or elimination. Let's use substitution.

First, solve equation (2) for one of the variables. We'll solve for x:

x = 5 - y

Now, substitute this expression for x into equation (1):

1/x + 1/y = 5/6

1/(5 - y) + 1/y = 5/6

Now, let's find a common denominator for the fractions:

[(5 - y) / (y(5 - y))] + [(5 - y) / (y(5 - y))] = 5/6

Now, we can add the fractions:

(2(5 - y)) / (y(5 - y)) = 5/6

Now, cross-multiply:

12(5 - y) = 5y

Distribute the 12 on the left side:

60 - 12y = 5y

Now, add 12y to both sides of the equation:

60 = 17y

Now, divide by 17 to solve for y:

y = 60 / 17

Now that we have found the value of y, we can substitute it back into the equation (2) to find x:

x = 5 - y x = 5 - (60 / 17)

Now, you can calculate the value of x:

x ≈ 5 - 3.5294 ≈ 1.4706

So, the solution to the system of equations is approximately:

x ≈ 1.4706 y ≈ 60/17