Question

Помогите розвязать систему уравнений: x-y=4 1/x+1/y=2/3 Помогите!!!

Answer 1

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Answer 2

Solving the System of Equations

To solve the system of equations x - y = 4 and 1/x + 1/y = 2/3, we can use the substitution method.

First, let's solve the equation x - y = 4 for x: x = y + 4.

Now, substitute x = y + 4 into the second equation 1/x + 1/y = 2/3: 1/(y + 4) + 1/y = 2/3.

Multiply through by 3y(y + 4) to clear the fractions: 3y + 3(y + 4) = 2y(y + 4).

Expand and simplify: 3y + 3y + 12 = 2y^2 + 8y, 6y + 12 = 2y^2 + 8y, 0 = 2y^2 + 8y - 6y - 12, 0 = 2y^2 + 2y - 12, 0 = y^2 + y - 6.

Now, we can solve for y using the quadratic formula: y = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = 1, and c = -6.

Plugging in the values: y = (-1 ± √(1^2 - 4*1*(-6))) / (2*1), y = (-1 ± √(1 + 24)) / 2, y = (-1 ± √25) / 2, y = (-1 ± 5) / 2.

So, we have two possible values for y: y = (-1 + 5) / 2 = 2, y = (-1 - 5) / 2 = -3.

Now, we can find the corresponding values of x using the equation x = y + 4: For y = 2, x = 2 + 4 = 6, For y = -3, x = -3 + 4 = 1.

Therefore, the solutions to the system of equations are: x = 6, y = 2 and x = 1, y = -3.