We are given two equations: $x - y = -1$ $-1 = x^3 + 1$ We need to solve for $x$ and $y$.

1. Problem Description

We are given two equations:

$x - y = -1$

$-1 = x^3 + 1$

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

2. Solution Steps

First, let's solve the second equation for $x$:

$-1 = x^3 + 1$

Subtract 1 from both sides:

$-1 - 1 = x^3 + 1 - 1$

$-2 = x^3$

Take the cube root of both sides:

$x = \sqrt[3]{-2}$

Now, let's substitute the value of $x$ into the first equation:

$x - y = -1$

$\sqrt[3]{-2} - y = -1$

Add $y$ and $1$ to both sides:

$\sqrt[3]{-2} + 1 = y$

$y = 1 + \sqrt[3]{-2}$

$y = 1 - \sqrt[3]{2}$

3. Final Answer

$x = \sqrt[3]{-2}$

$y = 1 - \sqrt[3]{2}$