Question

Xy+x=9 xy+y=8 решите систему уравнений.

Answer 1

Ответ:

{х1=3

х2=-3

у3=9

{х1=8

у2=4

у3=4

Answer 2

To solve the system of equations:

1. Xy + x = 9
2. xy + y = 8

We can use the method of substitution or elimination to find the values of x and y.

Method 1: Substitution

Step 1: Solve one equation for one variable in terms of the other variable. From equation (1), we can express x in terms of y: x = 9 - Xy

Step 2: Substitute the value of x from Step 1 into equation (2): (9 - Xy)y + y = 8

Step 3: Simplify and solve for y: 9y - Xy^2 + y = 8 y(9 - Xy + 1) = 8 y(10 - Xy) = 8 y = 8 / (10 - Xy)

Step 4: Substitute the value of y from Step 3 into the equation for x (from Step 1): x = 9 - X(8 / (10 - Xy))

Method 2: Elimination

Step 1: Multiply equation (1) by y and equation (2) by x to make the coefficients of xy equal: y(Xy + x) = 9y x(xy + y) = 8x

Step 2: Expand and rearrange the equations: Xy^2 + xy = 9y x^2y + xy = 8x

Step 3: Subtract the first equation from the second equation to eliminate xy: x^2y + xy - (Xy^2 + xy) = 8x - 9y x^2y - Xy^2 = 8x - 9y

Step 4: Factor out y on the left side: y(x^2 - Xy) = 8x - 9y

Step 5: Divide both sides by (x^2 - Xy) to solve for y: y = (8x - 9y) / (x^2 - Xy)

Step 6: Substitute the value of y from Step 5 into equation (1) and solve for x: X((8x - 9y) / (x^2 - Xy)) + x = 9

Now we have an equation involving only x, and we can solve for x. Once we have the value of x, we can find the corresponding value of y using either equation (1) or (2).

Please note that the system of equations provided is nonlinear, and solving for exact numerical solutions may require further simplification or approximation. The values of x and y depend on the value of X, and the solutions might be complex or have multiple solutions for certain values of X.