Question

Система 1/x+1/y=5/6. 1/x-1/y=1/6

Answer 1

1/y=-1/x+5/6. 1/x+1/x-5/6=1/6
1/y=-1/x+5/6. 2/x=1
x=0,5
1/y=-1/0,5+5/6
1/y=-2+5/6
1/y=-7/6
-7y=6
y=-6/7
ответ x=0,5 y=-6/7.

Answer 2

To solve the given system of equations:

1/x + 1/y = 5/6 ...(Equation 1) 1/x - 1/y = 1/6 ...(Equation 2)

We can use a method called elimination or substitution to solve this system. Here, I'll use the elimination method.

Step 1: Multiply Equation 2 by (1) and Equation 1 by (1), so we have:

(1/x - 1/y) = (1/6) ...(Equation 2) (1/x + 1/y) = (5/6) ...(Equation 1)

Step 2: Add the two equations together:

[(1/x - 1/y) + (1/x + 1/y)] = (1/6) + (5/6) 2/x = 6/6 2/x = 1

Step 3: Take the reciprocal of both sides:

x/2 = 1/1

Step 4: Multiply both sides by 2:

(x/2) * 2 = (1/1) * 2 x = 2

Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y.

Using Equation 1:

1/x + 1/y = 5/6

Substituting x = 2:

1/2 + 1/y = 5/6

Multiplying both sides by 6 to eliminate the fractions:

3 + 6/y = 5

Subtracting 3 from both sides:

6/y = 5 - 3 6/y = 2

Taking the reciprocal of both sides:

y/6 = 1/2

Multiplying both sides by 6:

(y/6) * 6 = (1/2) * 6 y = 3

Therefore, the solution to the system of equations is x = 2 and y = 3.