Question

X-y=4(x-1)(y+1)=2xy+3

Answer 1

Х=4-у
подставляем во второе
(4-у-1)(у+1)=2у(4+у)+3
3у+3+у²+у=8у+у²+3
у²+4у-8у-у²=3-3
-4у=0
4у=0
у=0
х=4+0=4

Answer 2

It seems like you have a system of equations with two variables, x and y. Let's solve it step by step.

The given system of equations is:

1. $x - y = 4$
2. $(x - 1)(y + 1) = 2xy + 3$

Let's start by solving the first equation for one variable and then substitute it into the second equation:

From equation 1, we have: $x = y + 4$

Now, substitute this value of $x$ into equation 2:

$(y + 4 - 1)(y + 1) = 2(y + 4)y + 3$

Simplify the equation:

$(y + 3)(y + 1) = 2y^2 + 8y + 3$

Expand the left side:

$y^2 + 4y + 3 = 2y^2 + 8y + 3$

Now, subtract $2y^2 + 8y + 3$ from both sides:

$y^2 + 4y + 3 - 2y^2 - 8y - 3 = 0$

Simplify:

$-y^2 - 4y = 0$

Divide by -1 (this doesn't change the solutions):

$y^2 + 4y = 0$

Factor out $y$:

$y(y + 4) = 0$

This gives us two possible solutions for $y$:

1. $y = 0$
2. $y = -4$

Now that we have the possible values for $y$, we can substitute them back into the equation $x = y + 4$ to find the corresponding values of $x$:

For $y = 0$, $x = 0 + 4 = 4$. For $y = -4$, $x = -4 + 4 = 0$.

So, the solutions to the system of equations are:

1. $x = 4$, $y = 0$
2. $x = 0$, $y = -4$