We are given a system of two equations: $x - y = -1$ $y = x^2 + 1$ We need to solve for $x$ and $y$.

1. Problem Description

We are given a system of two equations:

$x - y = -1$

$y = x^2 + 1$

We need to solve for $x$ and $y$.

2. Solution Steps

We can substitute the second equation into the first equation to eliminate $y$.

From the first equation, $y = x+1$.

Substituting this into the second equation, we have

$x + 1 = x^2 + 1$

$x^2 - x = 0$

$x(x - 1) = 0$

Thus, $x = 0$ or $x = 1$.

If $x = 0$, then $y = x^2 + 1 = 0^2 + 1 = 1$.

If $x = 1$, then $y = x^2 + 1 = 1^2 + 1 = 2$.

Therefore, the solutions are $(0, 1)$ and $(1, 2)$.

We can check these solutions with the first equation:

If $x = 0$ and $y = 1$, then $x - y = 0 - 1 = -1$, which is true.

If $x = 1$ and $y = 2$, then $x - y = 1 - 2 = -1$, which is true.

3. Final Answer

The solutions are $(0, 1)$ and $(1, 2)$.