Question

X^2-y^2 = 5 x+y = -1

Answer 1

Ответ:

x=-1-y

(-1-y)²-y²=5

1+2y+y²-y²=5

2y+1=5

2y=4

y=2

x=-1-2=-3

Answer 2

To solve the system of equations:

1. $x^2 - y^2 = 5$
2. $x + y = -1$

We can use the method of substitution. Let's solve the second equation for one of the variables and then substitute it into the first equation:

From equation (2), we can express $y$ in terms of $x$: $y = -1 - x$

Now, substitute this expression for $y$ into equation (1): $x^2 - (-1 - x)^2 = 5$

Now, expand and solve for $x$:

$x^2 - (1 + 2x + x^2) = 5$

Combine like terms:

$x^2 - 1 - 2x - x^2 = 5$

The $x^2$ terms cancel out:

$-1 - 2x = 5$

Add 1 to both sides:

$-2x = 6$

Divide both sides by -2:

$x = -3$

Now that we've found $x$, we can substitute it back into equation (2) to find $y$:

$x + y = -1$ $-3 + y = -1$

Add 3 to both sides:

$y = 2$

So, the solution to the system of equations is $x = -3$ and $y = 2$.