Question

Решите систему уравнений:(срочно нужно и правильно). Заранее спасибо

Answer 1

Решение во вложении. Должно быть понятно.

Answer 2

Solving the System of Equations

To solve the system of equations, we need to find the values of x and y that satisfy both equations. Here is the system of equations you provided:

Equation 1: x - xy = -3 Equation 2: y + xy = 8

To solve this system, we can use various methods such as substitution, elimination, or matrix methods. Let's solve it using the substitution method.

Substitution Method

Step 1: Solve Equation 1 for x in terms of y: x = -3 + xy

Step 2: Substitute the value of x from Step 1 into Equation 2: y + (-3 + xy)y = 8

Simplifying the equation: y - 3y + xy^2 = 8

Step 3: Rearrange the equation: xy^2 - 3y + y - 8 = 0

Step 4: Combine like terms: xy^2 - 2y - 8 = 0

Now, we have a quadratic equation in terms of y. To solve for y, we can use the quadratic formula:

y = (-b ± √(b^2 - 4ac)) / (2a)

Comparing the equation to the quadratic formula, we have: a = x, b = -2, c = -8

Plugging in the values, we get: y = (-(-2) ± √((-2)^2 - 4(x)(-8))) / (2x)

Simplifying further: y = (2 ± √(4 + 32x)) / (2x) y = (1 ± √(1 + 8x)) / x

Now, we have the value of y in terms of x. We can substitute this value back into Equation 1 to solve for x.

Conclusion

To summarize, we used the substitution method to solve the system of equations. We obtained the value of y in terms of x, and then substituted it back into Equation 1 to solve for x.