Question

{(х-2)у-х(у+1)=2-3 (х-2){(х+5)у-у(х-2)=-42+4(х+5)Решите систему уравнений.​

Answer 1

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Answer 2

To solve the system of equations, we'll first simplify the equations and then find the values of x and y that satisfy both equations. Let's proceed step by step:

1. Simplify the equations:

Equation 1: (x - 2) * y - x * (y + 1) = 2 - 3(x - 2)

Expanding the left-hand side: xy - 2y - xy - x = 2 - 3x + 6

Simplifying and combining like terms: -2y - x = 8 - 3x

Equation 2: (x + 5) * y - y * (x - 2) = -42 + 4(x + 5)

Expanding the left-hand side: xy + 5y - xy + 2y = -42 + 4x + 20

Simplifying and combining like terms: 7y = -22 + 4x

2. Now, we have the following two equations:

Equation A: -2y - x = 8 - 3x Equation B: 7y = -22 + 4x

3. Next, we can eliminate one of the variables (x or y) by solving one of the equations for either variable and then substituting it into the other equation. We'll solve Equation A for x:

From Equation A: x = -2y - (8 - 3x)

Simplifying: x = -2y - 8 + 3x

Move the x term to the left side: x - 3x = -2y - 8

Combine like terms: -2x = -2y - 8

Divide by -2: x = y + 4

4. Now, substitute the value of x (from the equation we just derived) into Equation B:

7y = -22 + 4(y + 4)

Distribute the 4 on the right side: 7y = -22 + 4y + 16

Combine like terms: 7y - 4y = -22 + 16

Simplify: 3y = -6

Divide by 3: y = -2

5. Finally, substitute the value of y back into the equation we derived in step 4 to find x:

x = (-2) + 4 x = 2

So, the solution to the system of equations is x = 2 and y = -2.