{ 1/x+1/y=1/6 5x-y=9

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вопрос

To solve this system of equations, we can start by solving the second equation for y in terms of x:

5x - y = 9
y = 5x - 9

Now we can substitute this expression for y into the first equation:

1/x + 1/(5x - 9) = 1/6

Multiplying through by 6x(5x - 9) to clear the fractions, we get:

6(5x - 9) + 6x = x(5x - 9)
30x - 54 + 6x = 5x^2 - 9x
36x - 54 = 5x^2 - 9x
36x - 54 = 5x^2 - 9x

Rearrange the equation to get a quadratic equation:

5x^2 - 45x + 54 = 0

Now we can solve this quadratic equation for x using the quadratic formula:

x = [-(-45) ± √((-45)^2 - 4(5)(54))] / (2*5)
x = [45 ± √(2025 - 1080)] / 10
x = [45 ± √945] / 10
x = [45 ± 3√105] / 10
x = 3.9 or x = 3.0

Now that we have found the possible values for x, we can plug them back into the equation y = 5x - 9 to find the corresponding values for y:

For x = 3.9:
y = 5(3.9) - 9
y = 19.5 - 9
y = 10.5

For x = 3.0:
y = 5(3) - 9
y = 15 - 9
y = 6

Therefore, the solutions to the system of equations are x = 3.9, y = 10.5 and x = 3.0, y = 6.